Dissertations / Theses: 'Compressible and incompressible fluids'

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Bocchi, Edoardo. "Compressible-incompressible transitions in fluid mechanics : waves-structures interaction and rotating fluids." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0279/document.

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Ce manuscrit porte sur les transitions compressible-incompressible dans les équations aux dérivées partielles de la mécanique des fluides. On s'intéresse à deux problèmes : les structures flottantes et les fluides en rotation. Dans le premier problème, l'introduction d'un objet flottant dans les vagues induit une contrainte sur le fluide et les équations gouvernant le mouvement acquièrent une structure compressible-incompressible. Dans le deuxième problème, le mouvement de fluides géophysiques compressibles est influencé par la rotation de la Terre. L'étude de la limite à rotation rapide montre que le champ vectoriel de vitesse tend vers une configuration horizontale et incompressible.Les structures flottantes constituent un exemple particulier d'interaction fluide-structure, où un solide partiellement immergé flotte à la surface du fluide. Ce problème mathématique modélise le mouvement de convertisseurs d'énergie marine. En particulier, on s'intéresse aux bouées pilonnantes, installées proche de la côte où les modèles asymptotiques en eaux peu profondes sont valables. On étudie les équations de Saint-Venant axisymétriques en dimension deux avec un objet flottant à murs verticaux se déplaçant seulement verticalement. Les hypothèses sur le solide permettent de supprimer le problème à bord libre associé avec la ligne de contact entre l'air, le fluide et le solide. Les équations pour le fluide dans le domaine extérieur au solide sont donc écrites comme un problème au bord quasi-linéaire hyperbolique. Celui-ci est couplé avec une EDO non-linéaire du second ordre qui est dérivée de l'équation de Newton pour le mouvement libre du solide. On montre le caractère bien posé localement en temps du système couplé lorsque que les données initiales satisfont des conditions de compatibilité afin de générer des solutions régulières.Ensuite on considère une configuration particulière: le retour à l'équilibre. Il s'agit de considérer un solide partiellement immergé dans un fluide initialement au repos et de le laisser retourner à sa position d'équilibre. Pour cela, on utilise un modèle hydrodynamique différent, où les équations sont linearisées dans le domaine extérieur, tandis que les effets non-linéaires sont considérés en dessous du solide. Le mouvement du solide est décrit par une équation intégro-différentielle non-linéaire du second ordre qui justifie rigoureusement l'équation de Cummins, utilisée par les ingénieurs pour les mouvements des objets flottants. L'équation que l'on dérive améliore l'approche linéaire de Cummins en tenant compte des effets non-linéaires. On montre l'existence et l'unicité globale de la solution pour des données petites en utilisant la conservation de l'énergie du système fluide-structure.Dans la deuxième partie du manuscrit, on étudie les fluides en rotation rapide. Ce problème mathématique modélise le mouvement des flots géophysiques à grandes échelles influencés par la rotation de la Terre. Le mouvement est aussi affecté par la gravité, ce qui donne lieu à une stratification de la densité dans les fluides compressibles. La rotation génère de l'anisotropie dans les flots visqueux et la viscosité turbulente verticale tend vers zéro dans la limite à rotation rapide. Notre interêt porte sur ce problème de limite singulière en tenant compte des effets gravitationnels et compressibles. On étudie les équations de Navier-Stokes-Coriolis anisotropes compressibles avec force gravitationnelle dans la bande infinie horizontale avec une condition au bord de non glissement. Celle-ci et la force de Coriolis donnent lieu à l'apparition des couches d'Ekman proche du bord. Dans ce travail on considère des données initiales bien préparées. On montre un résultat de stabilité des solutions faibles globales pour des lois de pression particulières. La dynamique limite est décrite par une équation quasi-géostrophique visqueuse en dimension deux avec un terme d'amortissement qui tient compte des couches limites This manuscript deals with compressible-incompressible transitions arising in partial differential equations of fluid mechanics. We investigate two problems: floating structures and rotating fluids. In the first problem, the introduction of a floating object into water waves enforces a constraint on the fluid and the governing equations turn out to have a compressible-incompressible structure. In the second problem, the motion of geophysical compressible fluids is affected by the Earth's rotation and the study of the high rotation limit shows that the velocity vector field tends to be horizontal and with an incompressibility constraint.Floating structures are a particular example of fluid-structure interaction, in which a partially immersed solid is floating at the fluid surface. This mathematical problem models the motion of wave energy converters in sea water. In particular, we focus on heaving buoys, usually implemented in the near-shore zone, where the shallow water asymptotic models describe accurately the motion of waves. We study the two-dimensional nonlinear shallow water equations in the axisymmetric configuration in the presence of a floating object with vertical side-walls moving only vertically. The assumptions on the solid permit to avoid the free boundary problem associated with the moving contact line between the air, the water and the solid. Hence, in the domain exterior to the solid the fluid equations can be written as an hyperbolic quasilinear initial boundary value problem. This couples with a nonlinear second order ODE derived from Newton's law for the free solid motion. Local in time well-posedness of the coupled system is shown provided some compatibility conditions are satisfied by the initial data in order to generate smooth solutions.Afterwards, we address a particular configuration of this fluid-structure interaction: the return to equilibrium. It consists in releasing a partially immersed solid body into a fluid initially at rest and letting it evolve towards its equilibrium position. A different hydrodynamical model is used. In the exterior domain the equations are linearized but the nonlinear effects are taken into account under the solid. The equation for the solid motion becomes a nonlinear second order integro-differential equation which rigorously justifies the Cummins equation, assumed by engineers to govern the motion of floating objects. Moreover, the equation derived improves the linear approach of Cummins by taking into account the nonlinear effects. The global existence and uniqueness of the solution is shown for small data using the conservation of the energy of the fluid-structure system.In the second part of the manuscript, highly rotating fluids are studied. This mathematical problem models the motion of geophysical flows at large scales affected by the Earth's rotation, such as massive oceanic and atmospheric currents. The motion is also influenced by the gravity, which causes a stratification of the density in compressible fluids. The rotation generates anisotropy in viscous flows and the vertical turbulent viscosity tends to zero in the high rotation limit. Our interest lies in this singular limit problem taking into account gravitational and compressible effects. We study the compressible anisotropic Navier-Stokes-Coriolis equations with gravitational force in the horizontal infinite slab with no-slip boundary condition. Both this condition and the Coriolis force cause the apparition of Ekman layers near the boundary. They are taken into account in the analysis by adding corrector terms which decay in the interior of the domain. In this work well-prepared initial data are considered. A stability result of global weak solutions is shown for power-type pressure laws. The limit dynamics is described by a two-dimensional viscous quasi-geostrophic equation with a damping term that accounts for the boundary layers

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Pareja, Victor David. "IMPULSE FORMULATIONS OF THE EULER EQUATIONS FOR INCOMPRESSIBLE AND COMPRESSIBLE FLUIDS." Master's thesis, University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3265.

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The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case. M.S. Department of Mathematics Sciences Mathematical Science MS

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Chinarak, Theerarak. "Development of a time-based mass flow controller for compressible and incompressible fluids." Thesis, University of Bristol, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503923.

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In this thesis a new type of Mass Flow Controller (MFC) is designed, constructed and used. Whilst existing MFCs rely on either pressure loss or temperature rise measurements to estimate and control flows, this new device is based on measuring time, which is more easily and accurately monitored. The device adopts the 'bucket and stopwatch' method to deliver specific and constant masses at pre-set time intervals. By alerting the time intervals, the mass flow is precisely controlled.

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Yang, Zhiyan. "Numerical simulation of incompressible and compressible flow." Thesis, University of Sheffield, 1989. http://etheses.whiterose.ac.uk/3485/.

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This thesis describes the development of a numerical solution procedure which is valid for both incompressible flow and compressible flow at any Mach number. Most of the available numerical methods are for incompressible flow or compressible flow only and density is usually chosen as a main dependent variable by almost all the methods developed for compressible flow. This practice limits the range of the applicability of these methods since density changes can be very small when Mach number is low. Even for high Mach number flows the existing time-dependent methods may be inefficient and costly when only the finial steady-state is of concern. The presently developed numerical solution procedure, which is based on the SIMPLE algorithm, solves the steady-state form of the Navier-stokes equations, and pressure is chosen as a main dependent variable since the pressure changes are always relatively larger than the density changes. This choice makes it possible that the same set of variables can be used for both incompressible and compressible flows. It is believed that Reynolds stress models would give better performance in some cases such as recirculating flow, highly swirling flow and so on where the widely used two equation k-e model performs poorly. Hence, a comparative study of a Reynolds stress model and the k-e model has been undertaken to assess their performance in the case of highly swirling flows in vortex throttles. At the same time the relative performance of different wall treatments is also presented. It is generally accepted that no boundary conditions should be specified at the outflow boundary when the outflow is supersonic, and all the variables can be obtained by extrapolation. However, it has been found that this established principle on the outflow boundary conditions is misleading, and at least one variable should be specified at the outflow boundary. It is also shown that the central differencing scheme should be used for the pressure gradient no matter whether it is subsonic or supersonic flow.

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Baghaei, Masoud. "Research on fluidic oscillators under incompressible and compressible flow conditions." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669607.

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One of the main advantages of fluidic oscillators is that they do not have moving parts, which brings high reliability whenever being used in real applications. To use these devices in real applications, it is necessary to evaluate their performance, since each application requires a particular injected fluid momentum and frequency. In this PhD., the performance of a given fluidic oscillator is evaluated at different Reynolds numbers via a 3D-computational fluid dynamics (CFD) analysis under incompressible and compressible flow conditions. In the first stage, the net momentum applied to the incoming jet is compared with the dynamic maximum stagnation pressure in the mixing chamber, to the dynamic output mass flow, to the dynamic feedback channels mass flow, to the pressure acting to both feedback channels outlets, and to the mixing chamber inlet jet oscillation angle. A perfect correlation between these parameters is obtained, therefore indicating the oscillation is triggered by the pressure momentum term applied to the jet at the feedback channels outlets. The stagnation pressure fluctuations appearing at the mixing chamber inclined walls are responsible for the pressure momentum term acting at the feedback channels outlets, thus it is proved that the oscillations are pressure-driven. In the second stage, several performance parameters were numerically evaluated as a function of different internal modifications via using 3D-CFD simulations. The evaluation is based on studying the output mass flow frequency and amplitude whenever several internal geometry parameters are modified. The geometry modifications considered were the mixing chamber inlet and outlet widths, and the mixing chamber inlet and outlet wall inclination angles. The concept behind this is, to evaluate how much the fluidic oscillator internal dimensions affect the device's main characteristics, and to analyze which parts of the oscillator produce a higher impact on the fluidic oscillator output characteristics. For the different internal modifications, evaluated, special care is taken in studying the forces required to flip the jet. The entire study is performed for three different Reynolds numbers, 8711, 16034 and 32068. Among the conclusions reached it is to be highlighted that, for a given Reynolds number, modifying the internal shape affects the oscillation frequencies and amplitudes. Any oscillator internal modification generates a much relevant effect as Reynolds number increases. Under all conditions studied, it was observed that the fluidic oscillator is pressure-driven under incompressible flow conditions as discussed in the first and second stages. In the third stage, the feedback channel effect on the oscillator output mass flow frequency and amplitude under compressible flow conditions were evaluated. In order to bring light to this point, a set of three dimensional Direct Numerical Simulations under compressible flow conditions, are introduced in the present stage, four different feedback channel lengths and two inlet fluid velocities are considered. From the results obtained, it was observed that as the inlet velocity increases, the fluidic oscillator output mass flow frequency and amplitude increase. An increase of the feedback channel length decreases the output mass flow oscillating frequency. At high feedback channel lengths, the form of the main oscillation tends to disappear, the jet inside the mixing chamber simply actuates at high frequencies, for these cases, the mass flow and pressure signals are very scattered due to the pressure waves appearing on mixing chamber converging surfaces and both feedback channels at the same time. Once the FC length exceeds a certain threshold, the oscillation stops. Under compressible conditions, the oscillations are pressure-driven as previously stated for the incompressible cases. The forces due to the pressure are much stronger than the mass flow flowing along the feedback channels. El principal avantatge dels oscil·ladors fluídics es que no te parts mòbils, i això fa que sigui més fiable en aplicacions reals. Per tal d'aplicar aquests oscil·ladors en un cas concret, es necessari avaluar el seu comportament, doncs cada cas concret necessita una freqüència i quantitat de moviment donades. En el present doctorat s'ha analitzat mitjançant 3D-CFD, una configuració de oscil·lador fluídic per diferents números de Reynolds, diferents geometries internes i considerant el fluid com incompressible i compressible. Inicialment, la quantitat de moviment aplicada al jet entrant a la cambra de barreja, es comparada amb la pressió d'estancament dinàmica a les parets convergents de la cambra de barreja, amb el cabal màssic dinàmic que surt del actuador, amb el cabal màssic dinàmic que passa per els canals de realimentació, amb la pressió dinàmica que hi ha a la sortida dels canals de realimentació i amb el angle de oscil·lació del jet a l'entrada de la cambra de barreja. Tots aquests paràmetres es va veure que estaven correlacionats i això indicava que el origen de les oscil·lacions del jet era únic i era la pressió d'estancament a les parets convergents de la cambra de barreja, provant que les oscil·lacions son dirigides per gradients de pressió. Posteriorment es va fer el mateix tipus de estudi però modificant la amplada i angle de inclinació a l'entrada de la cambra de barreja i també modificant la amplada i angle de inclinació de les parets de sortida de la cambra de barreja. Aquestes quatre modificacions de la geometria interna es van fer per tres números de Reynolds diferents, 8711, 16034 i 32068. Entre les conclusions obtingudes cal destacar que, la freqüència i amplitud de oscil·lació del jet a la sortida del actuador pot ser modificada al variar les dimensions i angles interns de la cambra de barreja. Independentment del número de Reynolds estudiat i de la modificació interna considerada, es va comprovar que les oscil·lacions estaven dirigides per els gradients de pressió existents entre les dos sortides dels conductes de realimentació. L'efecte generat per qualsevol modificació interna era sempre més rellevant a números de Reynolds alts. En la tercera fase de la tesi el fluid es va considerar com a compressible subsònic, i es va avaluar els efectes de la modificació de la longitud dels canals de realimentació, sobre la freqüència i amplitud del flux que surt del oscil·lador. Quatre diferents longituds i dos números de Mach van ser avaluats. Al augmentar la longitud del canal de realimentació, la freqüència i amplitud de la oscil·lació disminueix, la oscil·lació tendeix a ser mes caòtica, apareixen altes freqüències que fan que el jet fluctuï en lloc de oscil·lar, de fet a partir de una certa longitud les oscil·lacions desapareixen i només hi han fluctuacions. Aquestes fluctuacions apareixen abans per elevats números de Mach. Les oscil·lacions son degudes a gradients de pressió, al igual que en el cas de fluid incompressible. De fet, per fluid compressible, el cabal màssic que passa per els canals de realimentació, juga un paper menys rellevant que en el cas de fluid incompressible.

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Courtin, Victor. "Extensions of some approximate Riemann Solvers for the computation of mixed incompressible-compressible flows." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM041.

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Dans cette thèse, on s'intéresse à la simulation d'écoulements compressibles à l'aide de méthodes numériques implicites de type solveurs de Riemann, telles que la méthode de Roe ou le schéma HLLC. L'objectif est de développer des extensions faible nombre de Mach afin de préserver la précision des solutions discrètes dans la limite bas Mach. Ce type d'écoulement est souvent rencontré dans la simulation de configurations industrielles, caractérisées par la présence de zones plus ou moins étendues à faible vitesse.On se focalise sur la composante hyperbolique des équations de Navier-Stokes, qui constitue le cœur du problème d'analyse numérique abordé dans cette thèse, les équations d'Euler. On y expose une analyse approfondie et détaillée retraçant un sujet de recherche vieux de plusieurs décennies, qui présente encore d'importants défis, même pour ce modèle académique. La littérature recense un grand nombre d'extensions possibles pour le schéma de Roe, qui sont généralement faciles à implémenter. Ces extensions consistent à modifier certains termes de la dissipation numérique, en amplifiant ou diminuant leur contribution dans la limite faible nombre de Mach (on parle de « rescaling » de la dissipation numérique). Elles permettent par ailleurs d'obtenir une solution discrète compressible approchant la solution analytique issue de la théorie du potentiel pour le problème incompressible, sans pour autant introduire une détérioration des résultats dans le régime compressible. La capture des ondes de choc pour les écoulements transsoniques et supersoniques reste quasiment inchangée. Cependant, il existe plusieurs études suggérant de faire preuve de vigilance quant au choix de la formulation de ce type de correction. Il est connu de la littérature que des pertes de stabilité numérique sont généralement observées, ainsi que des risques d'apparition de problèmes de découplage vitesse-pression, détériorant fortement la précision globale de la solution discrète dans les faibles vitesses.Ces travaux se fondent sur deux corrections très différentes du schéma de Roe, issues de la littérature scientifique, et qui présentent des propriétés discrètes distinctes. La première approche, proposée par C.-C. Rossow, amplifie les sauts de pression en introduisant une vitesse artificielle du son, tandis que la seconde, développée par F. Rieper, vise à uniquement atténuer les sauts de vitesse. Ces deux approches illustrent deux stratégies majeures fréquemment utilisées dans les extensions à faible nombre de Mach. Nous commençons tout d'abord par l'analyse asymptotique discrète de l'approche proposée par C.-C. Rossow non publiée dans la littérature, en abordant également la formulation de la condition de stabilité au sens de von Neumann. On montre que cette correction évite l'écueil du découplage vitesse-pression. Ensuite, nous présentons une méthode numérique, visant à construire des phases implicites exactes nécessaires à l'intégration temporelle, en utilisant la différentiation algorithmique et un solveur direct. Ces techniques nous permettent de contourner la contrainte très stricte de stabilité sur le pas de temps, et d'obtenir des solutions discrètes en quelques centaines d'itérations, et ce même pour des écoulements à très faible nombre de Mach. La généralisation de ces travaux au schéma HLLC se fait ensuite en poursuivant l'analyse de la structure d'onde faite par M. Pelanti. Ces travaux révèlent une profonde similarité entre les dissipations numériques de ces méthodes. En particulier, nous dérivons un formalisme commun entre ces deux schémas, afin de simplifier les analyses, et la transposition d'une correction d'un solveur de Riemann approché à l'autre, au sens d'une relation très claire entre les deux méthodes. Cette analyse nous permet en particulier de dériver le schéma HLLC-Rossow, mais également d'expliciter l'expression de la matrice de viscosité du schéma HLLC, qui exhibe une ressemblance intéressante avec celle du schéma Roe In this thesis, we focus on the simulation of compressible flows using implicit Godunov-type methods, such as the Roe method or the HLLC scheme. The objective is to develop low Mach number extensions that preserve the accuracy of discrete solutions in the low Mach number limit. This type of flow is frequently encountered in the simulation of industrial configurations, which are often characterized by the presence of more or less extensive low-speed areas.We focus on the hyperbolic component of the Navier-Stokes equations, which form the core of the numerical analysis problem addressed in this thesis, the Euler equations. We present an in-depth and detailed analysis of research topic that has been the subject of investigations for decades, and which continues to present significant challenges, even for this academic model. A review of the literature reveals a large number of possible extensions to the Roe scheme, which are generally easy to implement. These involve modifying specific terms of the numerical dissipation, either by amplifying or by diminishing their contribution in the low Mach number limit (also known as a rescaling of the numerical dissipation). They also enable us to obtain a discrete compressible solution that approaches the analytical solution derived from potential theory for the incompressible problem, without introducing any deterioration in the results in the compressible regime. The capture of shock waves for transonic and supersonic flows remains almost unaltered. However, there are a number of studies suggesting that care should be taken in the choice of formulation for this type of correction. It is well documented in the literature that losses in numerical stability are generally observed, as well as the risk of velocity-pressure decoupling problems appearing, which can significantly deteriorate the overall accuracy of the discrete solution for low-speed flows.This work is based on two very different corrections of the Roe scheme, taken from the scientific literature, and highlighting distinct discrete properties. The first approach, proposed by C.-C. Rossow, amplifies pressure jumps by introducing an artificial speed of sound, whereas the second approach, developed by F. Rieper, aims to attenuate velocity jumps exclusively. These two approaches illustrate two major strategies frequently used in low-Mach extensions. We begin with a discrete asymptotic analysis of the approach proposed by C.-C. Rossow, which has not been published in the literature, including the formulation of the von Neumann stability condition. It is demonstrated that this correction avoids the issue of pressure- velocity decoupling. Next, we present a numerical method for constructing the exact implicit phases required for time integration, using algorithmic differentiation and a direct solver. These techniques enable us to bypass the very strict stability constraint on the time step, thereby facilitating the acquisition of discrete solutions within a few hundred iterations, even for very low Mach number flows. The generalization of this work to the HLLC scheme is then made by continuing the wave structure analysis carried out by M. Pelanti. This work demonstrates a significant similarity between the numerical dissipations of these methods. In particular, a common formalism between these two schemes is derived, with the aim of simplifying the analyses, and transposing of a correction from one approximate Riemann solver to the other, in the sense of a very clear relationship between the two methods. In particular, this analysis enables us to derive the HLLC-Rossow scheme, but also to clarify the expression of the viscosity matrix of the HLLC scheme, which exhibits an interesting resemblance to that of the Roe scheme

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Choudhary, Aniruddha. "Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/51169.

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Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e., analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh. Ph. D.

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Merle, Xavier. "Résolution des équations de stabilité globale en régimes incompressible et compressible avec une méthode aux différences finies de haute précision." Phd thesis, Paris, ENSAM, 2009. http://pastel.archives-ouvertes.fr/pastel-00005302.

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La plupart des écoulements en dynamique des fluides génèrent ou rencontrent des phénomènes instationnaires. Dans le domaine de l'aérospatial, au cours de la mise au point de certains moteurs de fusées d'altitude, des instationnarités basses fréquences ont été observées. Ces phénomènes, liés à l'interaction entre l'onde de choc et la couche limite turbulente qui se développe sur les parois, peuvent engendrer des déformations de la tuyère ou des mouvements inopportuns par rapport à son système d'attache. De nombreux travaux ont ´et´e entrepris afin d'en déterminer l'origine. L'´etude de la stabilité entre dans ce cadre. Dans ce contexte, le propos de cette thèse est de développer un code de stabilité globale adapté aux écoulements en régime compressible et en géométrie curviligne afin d'étudier la stabilité de l'interaction au sein de la tuyère. La résolution du problème est assuré par un schéma aux différences finies de type DRP. Le code est validé à travers plusieurs cas-tests incompressibles, compressibles et en maillage curviligne. Ces configurations permettent également de souligner les avantages du schéma de discrétisation retenu par rapport `a d'autres solutions plus classiques utilisées généralement dans ce type de problèmes.

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Martínez, Germán Andrés Gaviria. "Towards natural transition in compressible boundary layers." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/18/18148/tde-24052017-114027/.

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In this work, a DNS code was developed to investigate problems on transition in subsonic compressible boundary layer on a flat plate. Code validation tests were performed for linear and nonlinear stages of transition, on incompressible and compressible regimes. The focus of the present work is to investigate natural transition in subsonic boundary layers modeled by wave packets; and perform a preliminary study of transition induced by white noise. Three main problems were considered, namely, a DNS simulation and analysis of the ex- periment (MEDEIROS; GASTER, 1999b) of wave packet evolution on incompressible boundary layer, the influence of compressibility on wave packet evolution at subsonic Mach numbers and finally, a preliminary study of the evolution of a white noise perturbation in the boundary layer at Mach 0.2 and Mach 0.9. Comparisons between numerical and experimental results show remarkably good agreement in the linear and nonlinear stages, in both, spatial and Fourier spaces. A numerical simulation of this experiment and the analysis carried out is not available in the literature for wave packets in the incompressible boundary layer. The nonlinear modal analysis performed established the existence of tuned fundamental and subharmonic resonance of H-type and K-type in the packet. Influence of compressibility in the wave packet evolution was here investigated in boundary layers at Mach 0.7 and Mach 0.9. There are no works reported in the literature on wave packets in compressible subsonic boundary layer. In the linear regime, the oblique modes were the most unstable for Mach > 0.7, as expected by the results of the literature. In the nonlinear regime, strong streaks were observed, associated with low frequency modes that eventually decay downstream. An isolated wave packet at Mach 0.9 showed nonlinear amplification only in the subharmonic band, which may be associated to H-type or detuned resonance. However this packet has a relatively stable character. On the other hand, at Mach 0.9 spanwise interaction of wave packet pairs were more unstable than the isolated case, because stable modes for the isolated packet evolution becomes unstable in the wave packet interaction. This scenario evidenced the presence of oblique transition. Finally, the nonlinear evolution of the same white noise disturbance at Mach 0.2 and Mach 0.9 were observed to be completely different. In the incompressible boundary layer localized lambda vortex structures were observed, that could be associated to the local presence of H-type and/or K-type resonance. In the compressible regime, longitudinal vortex structures distributed across the entire domain seemed to be linked to oblique transition. In the white noise evolution, compressibility seems to have a stronger effect than in the wave packet evolution. In the conditions considered, the wave packet interaction appear to be a better representation of white noise compressible transition scenario. No presente trabalho, um código DNS (Direct Numerical Simulation) foi desenvolvido para abordar problemas de transição para turbulência em camada limite subsônica compressível em uma placa plana. Foram realizados testes de validação de código , nos regimes linear e não linear do processo de transição, nos regimes incompressível e compressível. O foco do presente trabalho é estudar transição natural modelada por meio de pacotes de onda em camada limite compressível subsônica, e realizar uma análise preliminar da transição induzida por ruído branco. Três assuntos principais foram considerados: uma simulação DNS e uma análise comparativa com o experimento (MEDEIROS; GASTER, 1999b) sobre a evolução de um pacote de ondas em camada limite incompressível, a influência da compressibilidade na evolução de pacotes de ondas no regime subsônico, e por último, um estudo preliminar da transição induzida por ruído branco em Mach 0.2 e Mach 0.9. As comparações realizadas entre a solução numérica e os dados experimentais mostram uma boa concordância, nos regimes linear e não linear, tanto no espaço físico quanto no espaço de Fourier. A simulação numérica deste experimento e a análise realizada neste trabalho, não são encontradas na literatura para o regime incompressível. A análise modal não linear aplicada aos resultados, permitiu identificar a presença das ressonâncias tipo H e tipo K no pacote de ondas. A influência da compressibilidade na evolução dos pacotes de onda foi estudada em Mach 0.7 e Mach 0.9. Na literatura não há trabalhos sobre pacotes de ondas no regime sub- sônico. No regime linear da transição, os modos oblíquos resultam ser os mais instáveis para Mach > 0.7, como era de esperar, de acordo com os resultados da literatura. No regime não linear, foram observadas estrias de moderada amplitude, associadas com modos de baixa frequência que acabam decaindo. O pacote de ondas em Mach 0.9 apresentou amplificação não linear somente na banda subharmônica, que pode ser associada com transição tipo H ou ressonância dessintonizada. No entanto, o comportamento geral neste regime é estabilizante. Por sua vez, a interação entre pacotes de ondas em Mach 0.9 mostrou um comportamento desestabilizante, pois a interação acaba gerando amplificação não linear em modos que decaem no pacote isolado. Os modos amplificados sugerem a presença do mecanismo de transição oblíqua. Finalmente, a evolução da mesma perturbação constituída por ruído branco em Mach 0.2 e Mach 0.9, resultaram ser completamente diferentes. Na camada limite incompressível foram observados vórtices tipo lambda, que poderiam ser gerados pela presença localizada das ressonâncias tipo H e/ou tipo K. No regime compressível foram observados vórtices distribuidos em todo o domínio, o que sugere a presença da transição oblíqua. Na transição gerada por ruído branco a compressibilidade teve uma influência maior que no pacote de ondas. Nas condições estudadas, a interação entre pacotes de ondas parece ser uma melhor representação do ruído branco no regime compressível.

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Pontaza, Juan Pablo. "Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/288.

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We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

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Dainese, Marie-Pierre. "Simulation d'écoulements de fluide compressible en géométrie complexe : contribution à l'étude des schémas de discrétisation et d'algorithmes semi-implicites." Toulouse, ENSAE, 1994. http://www.theses.fr/1994ESAE0016.

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Cette thèse concerne la résolution numérique des équations de Navier-Stokes formulées en coordonnées curvilignes et discrétisées par la méthode des volumes finis sur des maillages non décalés. L'étude contribue à la compréhension, la validation et la mise en oeuvre des schémas de discrétisation de la convection d'ordre élevé et des algorithmes de couplage pression vitesse semi-implicites pour les fluides incompressibles. La comparaison des diverses méthodes ne permet pas de mettre en évidence une technique de discrétisation ni de couplage systématiquement plus satisfaisante que les autres. La présentation des résultats cherche à mettre en évidence les différences de comportement des méthodes. Les implantations des schémas de discrétisation (centré, QUICK, amont au second ordre et CONDIF) qui permettent une résolution stable sont comparées sur les cas de la cavité carrée entraînée et le sillage laminaire d'un cylindre circulaire, dans des configurations de calcul éprouvantes pour la précision des résultats et la stabilité de résolution. Les algorithmes de résolution semi-implicites (SIMPLE, SIMPLEC, SIMPLER et PISO) sont présentés à partir d'une formulation générales de l'équation de correction de pression. L'étude des performances des divers algorithmes est paramétrée par le coefficient de sous relaxation de la vitesse, le schéma de discrétisation employé, le raffinement du maillage et le type de conditions aux limites sur la vitesse.

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12

Mitra, Sourav. "Analysis and control of some fluid models with variable density." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30162/document.

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Dans cette thèse, nous étudions des modèles mathématiques concernant certains problèmes d'écoulement de fluide à densité variable. Le premier chapitre résume l'ensemble de la thèse et se concentre sur les résultats obtenus, la nouveauté et la comparaison avec la littérature existante. Dans le deuxième chapitre, nous étudions la stabilisation locale des équations non homogènes de Navier-Stokes dans un canal 2d autour du flot de Poiseuille. Nous concevons un contrôle feedback de la vitesse qui agit sur l'entrée du domaine de sorte que la vitesse et la densité du fluide soient stabilisées autour du flot de Poiseuille, à condition que la densité initiale soit donnée par une constante additionnée d'une perturbation dont le support se situe loin du bord latéral du canal. Dans le troisième chapitre, nous étudions un système couplant les équations de Navier-Stokes compressibles à une structure élastique située à la frontière du domaine fluide. Nous prouvons l'existence locale de solutions solides pour ce système couplé. Dans le quatrième chapitre, notre objectif est d'étudier la nulle- contrôlabilité d'un problemè d'interaction fluide-structure linéarisé dans un canal bi dimensional. L'écoulement du fluide est ici modélisé par les équations de Navier-Stokes compressibles. En ce qui concerne la structure, nous considérons une poutre de type Euler-Bernoulli amortie située sur une partie du bord. Dans ce chapitre, nous établissons une inégalité d'observabilité pour le problème considéré d'interaction fluid-structure linéarisé qui constitue le premier pas vers la preuve de la nulle contrôlabilité du système In this thesis we study mathematical models concerning some fluid flow problems with variable density. The first chapter is a summary of the entire thesis and focuses on the results obtained, novelty and comparison with the existing literature. In the second chapter we study the local stabilization of the non-homogeneous Navier-Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that both the fluid velocity and density are stabilized around Poiseuille flow provided the initial density is given by a constant added with a perturbation, such that the perturbation is supported away from the lateral boundary of the channel. In the third chapter we prove the local in time existence of strong solutions for a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. In the fourth chapter our objective is to study the null controllability of a linearized compressible fluid structure interaction problem in a 2d channel where the structure is elastic and located at the fluid boundary. In this chapter we establish an observability inequality for the linearized fluid structure interaction problem under consideration which is the first step towards the direction of proving the null controllability of the system

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Sadoudi, Yannis. "Simulation numérique de l'interaction soufflante/nacelle en présence de vent de travers." Thesis, Toulouse, ISAE, 2016. http://www.theses.fr/2016ESAE0005/document.

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La conception des nacelles doit répondre à des contraintes géométriques d’encombrement mais aussi à des spécifications motoristes qui précisent les niveaux de performance exigés. Au sol, l’une des principales contraintes imposées par le motoriste concerne le niveau de distorsion de pression totale dans le plan fan quand la nacelle est soumise à un vent de travers. Dans le cas le plus limitant, c’est-à-dire lorsque la direction du vent est perpendiculaire à l’axe de la nacelle, il se produit un décollement au niveau de l’entrée d’air côté vent. L’hétérogénéité de l’écoulement crée des efforts instationnaires sur les aubes du fan. Ces efforts peuvent amener à un régime de pompage endommageant ainsi le moteur. De plus, la tendance actuelle est de réaliser des nacelles courtes, réduisant la distance qu’à l’écoulement pour s’homogénéiser avant d’impacter le fan, conduisant à un couplage entre le décollement et le fan. Le but de cette étude est de simuler numériquement l’écoulement intervenant dans une nacelle courte soumise à un vent de travers et d’étudier l’impact de la présence du fan. Tout d’abord, la définition de la distorsion est basée sur les grandeurs totales. Ainsi, la compréhension du comportement des grandeurs totales au voisinage d’une paroi et l’influence des paramètres numériques sur leur évolution est nécessaire. Une approche analytique et numérique sur plaque plane a permis d’évaluer le comportement des grandeurs totales à la frontière externe de la couche limite et l’influence des paramètres numériques RANS sur leur évolution. Cette étude a permis de choisir les paramètres numériques utilisés pour la simulation de la nacelle. Pour faire ressortir l’influence du fan sur la distorsion, deux types de simulations ont été menés : une simulation de nacelle isolée et une simulation de l’ensemble complet nacelle/fan respectivement comparées à un essai en soufflerie sur une maquette de nacelle isolée et à un essai de moteur complet à échelle 1 :1 réalisé en « soufflerie » à veine ouverte. La description correcte de la distorsion nécessite de prendre en compte les phénomènes de transition. Une méthode innovante de prise en compte de la transition par équations de transport est utilisée. Comme le coût de calcul de l’ensemble complet est prohibitif, la question du découplage du calcul en injectant une distorsion, issue d’une simulation de nacelle isolée, dans un calcul de fan isolé est discutée. La distorsion par vent de travers intervient lorsque l’avion est au sol. Par conséquent, l’impact de la présence du sol est étudié dans le cas de la nacelle isolée. Enfin, le critère de distorsion utilisé présente plusieurs défauts importants et peut être remis en cause. Une nouvelle méthode de mesure et de calcul estétudiée Inlet design must fulfill geometrical constraints and engine requirements. One of these requirementsis the homogeneity of the flow impacting the fan which is quantified by the distortionlevels of stagnation pressure. When the airplane is on the ground and ready to take-off, crosswindconditions are critical for the distorsion level. The most critical case is when the wind directionis normal to the engine axis. Subsonic and supersonic separations occur near the inlet lip. Theso-created heterogeneity produces an unsteady stress on the fan blades which can lead to surge.Furthermore, short inlets are designed nowadays reducing the distance available for the flow tohomogenize before the fan leading to a coupling between the fan and the separated flow region.The aim of this study is to numerically predict the flow in a short inlet under crosswind conditionsand to investigate the fan influence on the distortion. First of all, the distortion definition isbased on stagnation quantities. Therefore, the stagnation quantities behavior and the numericalparameters influence must be investigated. The behavior of the stagnation quantities near theboundary layer edge is studied with analytical and numerical approaches. The numerical parameterschosen for the inlet simulation come from the so-obtained results obtained. In order tohighlight the fan influence on the distortion, two kinds of simulations were proceeded and comparedto experimental results : an isolated inlet simulation and a inlet/fan simulation. To correctlypredict the distortion, transition has to be be taken into account. Therefore an innovative solutionusing transport equations is used. As the computation cost for the inlet/fan computation isprohibitive, the decoupling which consists in injecting on a isolated fan the distortion obtainedduring a isolated inlet computation, is discussed. In fact, crosswind conditions occur when theairplane is on the ground, thus, the ground influence over the inlet distortion is studied for anisolated inlet. Finally, the distortion criterion used in this study has evidenced some strong defectsand can be questioned. Another approach of measurement with another criterion definitionis investigated

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Rashid, Abu S. "Compressible magnetorheological fluids." abstract and full text PDF (UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1456488.

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15

Pretorius, Johannes Jacobus. "A network approach for the prediction of flow and flow splits within a gas turbine combustor." Diss., University of Pretoria, 2005. http://hdl.handle.net/2263/26712.

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The modern gas turbine engine industry needs a simpler and faster method to facilitate the design of gas turbine combustors due to the enormous costs of experimental test rigging and detailed computational fluid dynamics (CFD) simulations. Therefore, in the initial design phase, a couple of preliminary designs are conducted to establish initial values for combustor performance and geometric characteristics. In these preliminary designs, various one-dimensional models using analytical and empirical formulations may be used. One of the disadvantages of existing models is that they are typically geometric dependant, i.e. they apply only to the geometry they are derived for. Therefore the need for a more versatile design tool exists. In this work, which constitutes the first step in the development of such a versatile design tool, a single equation-set network simulation model to describe both steady state compressible and incompressible isothermal flow is developed. The continuity and momentum equations are solved through a hybrid type network model analogy which makes use of the SIMPLE pressure correction methodology. The code has the capability to efficiently compute flow through elements where the loss factor K is highly flow dependant and accurately describes variable area duct flow in the case of incompressible flow. The latter includes ducts with discontinuously varying flow sectional areas. Proper treatment of flow related non-linearities, such as flow friction, is facilitated in a natural manner in the proposed methodology. The proposed network method is implemented into a Windows based simulation package with a user interface. The ability of the proposed method to accurately model both compressible and incompressible flow is demonstrated through the analyses of a number of benchmark problems. It will be shown that the proposed methodology yields similar or improved results as compared to other’s work. The proposed method is applied to a research combustor to solve for isothermal flows and flow splits. The predicted flows were in relatively close agreement with measured data as well as detailed CFD analysis. Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2005. Mechanical and Aeronautical Engineering unrestricted

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16

Blank, Henrik. "Numerical methods for compressible and incompressible flow." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300125.

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Barker, Tobias. "Uniqueness results for viscous incompressible fluids." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:db1b3bb9-a764-406d-a186-5482827d64e8.

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First, we provide new classes of initial data, that grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. The main novelty here is the establishment of certain continuity properties near the initial time, for weak Leray-Hopf solutions with initial data in supercritical Besov spaces. The techniques used here build upon related ideas of Calderón. Secondly, we prove local regularity up to the at part of the boundary, for certain classes of solutions to the Navier-Stokes equations, provided that the velocity field belongs to L∞(-1; 0; L3, β(B(1) &xcap; &Ropf;3 +)) with 3 ≤ β < ∞. What enables us to build upon the work of Escauriaza, Seregin and &Scaron;verák [27] and Seregin [100] is the establishment of new scale-invariant estimates, new estimates for the pressure near the boundary and a convenient new ϵ-regularity criterion. Third, we show that if a weak Leray-Hopf solution in &Ropf;3 +×]0,∞[ has a finite blow-up time T, then necessarily limt↑T||v(·, t)||L3,β(&Ropf;3 +) = ∞ with 3 < β < ∞. The proof hinges on a rescaling procedure from Seregin's work [106], a new stability result for singular points on the boundary, suitable a priori estimates and a Liouville type theorem for parabolic operators developed by Escauriaza, Seregin and &Scaron;verák [27]. Finally, we investigate a notion of global-in-time solutions to the Navier- Stokes equations in &Ropf;3, with solenoidal initial data in the critical Besov space ?-1/44,∞(&Ropf;3), which has certain continuity properties with respect to weak&ast; convergence of the initial data. Such properties are motivated by the strategy used by Seregin [106] to show that if a weak Leray-Hopf solution in &Ropf;3×]0,∞[ has a finite blow-up time T, then necessarily limt↑T ||v(·, t)||L3(&Ropf;3) = ∞. We prove new decomposition results for Besov spaces, which are key in the conception and existence theory of such solutions.

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Pavlov, Dmitry Marsden Jerrold E. Marsden Jerrold E. Desbrun Mathieu. "Structure-preserving discretization of incompressible fluids /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05222009-125630.

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19

Kho, Cedric. "A unified formulation for mixed incompressible/compressible flows." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/MQ44017.pdf.

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20

Tain, Ludovic. "Compressor leading edges in incompressible and compressible flows." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/272432.

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21

Billaud, Friess Marie. "Eléments finis stabilisés pour des écoulements diphasiques compressible-incompressible." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00565815.

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Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en \oe uvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: - une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; - une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; \item et des grandeurs moyennées pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnels.

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22

Wadey, Philip David. "Goetler vortex instabilities of incompressible and compressible boundary layers." Thesis, University of Exeter, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253560.

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23

Huber, Jamison Jared. "Numerical Simulations of Incompressible and Compressible Transitional Turbine Flows." Thesis, North Dakota State University, 2014. https://hdl.handle.net/10365/27124.

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Accurate and reliable turbulence and transition models are needed for prediction heating loads in the hot section of the turbine, and predicting aerodynamic losses when designing new blade profiles. Two dimensional compressible flow simulations were conducted at North Dakota State University on a first stage turbine vane design. Surface pressure results were compared with experimental data collected at the University of North Dakota. Results showed an under prediction of the surface pressure on the suction surface of the vane. Two and three dimensional compressible flow simulations were also conducted at NDSU on an incident tolerant blade design to look at the effect of incidence angle, Reynolds number, and turbulence intensity on transition. Results from these simulations were compared with experimental data collected at UND. The results show good agreement at higher Reynolds numbers with discrepancies being seen on the suction surface of the blade at lower Reynolds numbers.

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Billaud, Marie. "Eléments finis stabilisés pour des écoulements diphasiques compressible-incompressible." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13872/document.

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Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en oeuvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; et des grandeurs moyennes pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnels In this work, we are interested in the numerical simulation of instationnary viscous flows of two immiscible fluids, separated by a mobile interface. In particular, flows without shock composed of a gas phase and a liquid phase are considered. In order to modelize such flows, an approach in which the gaz is described by compressible Navier-Stokes equations and the liquid by incompressible Navier-Stokes équations is proposed. The coupling between these two models is the originality and the stake of this thesis. To treat this important difficulty, a global (i.e. the same for each phase) and simple method is elaborated. In our procedure we propose, using the Navier-Stokes equations formulated in set of primitives unknowns (pressure, velocity and temperature), to elaborate a strategy that relies on the follow components: the stabilized finite element method to discretize spatially the Navier-Stokes equations; the Level Set method for tracking the interface precisely with a discontinuous Galerkin method to solve the associated transport equation; and some averaged quantities to treat the discontinuities at the interface. The good behaviour of this approach is performed on both one and two spatial dimensions

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Nersisyan, Hayk. "Contrôlabilité et stabilisation des équations d'Euler incompressible et compressible." Thesis, Cergy-Pontoise, 2011. http://www.theses.fr/2011CERG0531/document.

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Dans cette thèse, on étudie la contrôlabilité et la stabilisation de certaines équations aux dérivées partielles . On s'intéresse d'abord au problème du contrôle de l'équation d'Euler 3D incompressible par une force extérieure de dimension finie. Nous montrons que pour un choix approprié de l'espace de contrôle, la vitesse et la pression du fluide sont exactement contrôlables en projections. De plus, la vitesse est approximativement contrôlable. Nous montrons aussi que le système en question n'est pas exactement contrôlable par une force extérieure de dimension finie.On étudie aussi la contrôlabilité de l'équation d'Euler 3D compressible. Le contrôle est une force extérieure de dimension finie agissant uniquement sur l'équation de la vitesse. Nous montrons que la vitesse et la densité du fluide sont simultanément contrôlables. En particulier, le système est approximativement contrôlable et exactement contrôlable en projections. Dans la dernière partie, on étudie la stabilisation de l'équation d'Euler dans un cylindre infini.Nous montrons que pour toute solution stationnaire (c,0) du système d'Euler il existe un contrôle supporté dans une partie de la frontière du cylindre qui stabilise le système à (c,0) In this thesis, we study the controllability and stabilization of certain partial differential equations.We consider first the problem of control of the 3D incompressible Euler equationby an external force of finite dimension. We show that for an appropriate choice of control space, the velocity and the pressure of the fluid are exactly controllable in projections.Moreover, the velocity is approximately controllable. We also show that the system in question is not exactly controllable by a finite-dimensional external force.We also study the controllability of the 3D compressible Euler equation. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are simultaneously controllable. In particular, the system is approximately controllable and exactly controllable in projections.The last section of the thesis is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c,0) of the Euler system there is a control which is supported in a given bounded part of the boundary of the strip and stabilizes the system to (c,0)

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26

Kliegl, Markus Vinzenz. "Explorations in the mathematics of inviscid incompressible fluids." Thesis, Princeton University, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10010743.

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The main subject of this dissertation is smooth incompressible fluids. The emphasis is on the incompressible Euler equations in all of R 2 or R3, but many of the ideas and results can also be adapted to other hydrodynamic systems, such as the Navier-Stokes or surface quasi-geostrophic (SQG) equations. A second subject is the modeling of moving contact lines and dynamic contact angles in inviscid liquid-vapor-solid systems under surface tension. The dissertation is divided into three independent parts: First, we introduce notation and prove useful identities for studying incompressible fluids in a pointwise Lagrangian sense. The main purpose is to provide a unified treatment of results scattered across the literature. Furthermore, we prove several analogs of Constantin’s local pressure formula for other nonlocal operators, such as the Biot-Savart law and Leray projection. Also, we define and study properties of a Lagrangian locally compact Abelian group in terms of which some nonlocal formulas encountered in fluid dynamics may be interpreted as convolutions. Second, we apply the algebraic theory of scalar polynomial orthogonal invariants to the incompressible Euler equations in two and three dimensions. Using this framework, we give simplified proofs of results of Chae and Vieillefosse. We also investigate other uses of orthogonal transformations, such as diagonalizing the deformation tensor along a particle trajectory, and comment on relative advantages and disadvantages. These techniques are likely to be useful in other orthogonally invariant PDE systems as well. Third, we propose an idealized inviscid liquid-vapor-solid model for the macroscopic study of moving contact lines and dynamic contact angles. Previous work mostly addresses viscous systems and frequently ignores a singular stress present when the contact angle is not at its equilibrium value. We also examine and clarify the role that disjoining pressure plays and outline a program for further research.

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27

Das, Niranjan. "Some problem on wave motion on incompressible fluids." Thesis, University of North Bengal, 2004. http://hdl.handle.net/123456789/646.

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28

Enault, Séverine. "Modélisation de la propagation d'une tumeur en milieu faiblement compressible." Lyon, Ecole normale supérieure, 2010. http://www.theses.fr/2010ENSL0607.

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Dans cette thèse, on s’intéresse à la modélisation, à l’analyse mathématique et numérique de certains phénomènes biologiques. On a d’abord étudié l’effet de la compressibilité du tissu sain sur la progression d’une tumeur solide. Deux systèmes d’équations aux dérivées partielles découlent de cette modélisation selon la prise en compte de la compressibilité des cellules saines : un système incompressible et un système compressible. Après avoir étudié l'existence de solution pour ces deux systèmes, une comparaison numérique permet de quantifier l’effet de la compressibilité sur la croissance de la tumeur. Enﬁn, on s’est intéressé à la modélisation et à la simulation numérique du transport du mucus dans le poumon. L’étude numérique en 2D a mis en évidence l'importance du mouvement des cils de l'épithélium et a permis de préciser les termes dominants nécessaires à la mise en place d’un schéma numérique en 3D In this thesis, we are interested in modeling, mathematical analysis and numerical simulation of some biological phenomena. We ﬁrst study the compressibility effect of the healthy tissu on the invasivness of a tumor. Two systems of partial differential equations follow from this modeling depending on whether the compressibility of the healthy tissu is taken into account: an incompressible system and a compressible one. After the study of the existence of solution of both systems, a numerical comparison allows to quantify the compressibility effect on tumor growth. Finally, we model and simulate mucus motion in the lung. The numerical study in 2D shows the importance of the epithelium ciliated cells in this phenomenon and identiﬁes the leading terms and the leads to follow for the 3D algorithm

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29

Brock, S. T. H. "Fractal dimensions and their relationship to filtration characteristics." Thesis, Loughborough University, 2000. https://dspace.lboro.ac.uk/2134/13486.

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Work has been performed to characterise filtration systems according to their fractal properties and to construct agglomerates to mimic the filtration systems under scrutiny. The first objective was achieved by carrying out experiments examining the dead-end filtration of two separate mineral suspensions, namely calcite and talc. These minerals were chosen to represent typical incompressible (calcite) and compressible (talc) filtration systems, undergoing filtration using a range of pressures. The experimental apparatus produced filter cakes that could be sampled, sectioned and examined under high magnification. The second objective was met by developing a computer application that could construct simulated particle agglomerates in both two and three dimensions, using a seed agglomeration model as well as simulating filtration by means of a virtua1 filter cell. A large number of simulations were completed to mimic both the dead-end filtration and other agglomerate models. The computer application was also capable of characterising the fractal and Euclidean spatial nature of both the simulated and experimental particulate systems, using a variety of techniques. Euclidean spatial attributes such as porosity as well as fractal properties including surface roughness and a number of density fractal dimensions have been measured for both types of system and demonstrate that the conditions under which the trials were performed have a bearing on the final configuration of the structures. Results from both experimental and simulation work show that fractal dimensions offer a valid method of measuring the properties of filtration systems. Experimental results showed that as the filtering pressure was increased, the density fractal dimension for the system appeared to increase. This change in fractal dimension was also accompanied by a decrease in the porosity of the system (more so for talc than the calcite), confirming the compressibility of the materials under scrutiny. The characterisation of the sampled cakes also showed that the spatial characteristics vary within the individual slices of the sample,in agreement with modem filtration theory. Results from the simulations show that both the physical and fractal properties of the resulting structures varied with the parameters used to construct them. As a rule, as the particles in the simulations were able to move in a more diffusive manner (akin to Brownian motion), the agglomerates they formed had a more open, rugged structure. The simulation of filtration systems also showed a variation within the individual cake structures. In the case of the filtration simulations, the probability assigned to the particles' sticking to the growing agglomerate was the controlling factor. In addition, it was found that the simulated cakes had similar spatial properties to the experimental systems they were designed to replicate.

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RONZANI, ERNESTO RIBEIRO. "NUMERICAL SOLUTION OF COMPRESSIBLE AND INCOMPRESSIBLE FLOW IN IRREGULAR GEOMETRIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1996. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=18648@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO Este trabalho propõe um método numérico de solução de escoamentos de fluidos compressíveis e incompressíveis a qualquer número de Mach em geometrias irregulares. Um sistema bidimensional de coordenadas curvilíneas não-ortogonais,coincidentes com os contornos físicos é utilizado. Os componentes cartesianos de velocidade são usados nas equações da quantidade de movimento e os covariantes na equação da continuidade. Seleciona-se a técnica de volumes finitos para discretizar as equações de conservação relacionadas aos princípios físicos, em regime permanente devido esta preservar a propriedade conservativa das equações e a sua con sistência física no processo numérico. Adota-se a configuração de malha co-localizada, avaliando-se todas as variáveis dependentes nos pontos centrais dos volumes são avaliados com esquemas Power-Law e Quick. Especial atenção é dada ao tratamento numérico das condições de contorno. O problema do acoplamento massa específica-pressão-velocidade é solucionado usando-se uma combinação das equações da continuidade, de quantidade de movimento linear e de uma equação de estado, gerando duas equações de correção da pressão. A primeira corrige a massa específica e a pressão, a segunda, o fluxo de massa e a velocidade. Propõe-se uma modificação da equação da correção da velocidade usando um termo de compensação do erro obtido na sua avaliação a fim de acelerar a convergência. Utilizam-se vários tipos de interpolação da massa específica na face, para minimizar as atenuações das variáveis, causadas pela falsa difusão. Para a solução das equações algébricas resultantes usa-se o algoritmo TDMA linha por linha e um processo de correção por blocos para acelerar a convergência. O método proposto é verificado em seis problemas testes, através da comparação com os resultados analíticos e numéricos disponíveis na literatura. The present work consists in the development of a numerical method of solution of compressible and incompressible fluid flow for all speed in iregular geometries. A boundary-fitted two-dimensional nonorthogonal curvilinear coordinate systeam is utilized. The cartesian velocity components are the dependent variables in the momentum equations and covariant velocity components are used in the continuity equation. The finite-volume technique was selected to discretuze the steady-state physical phenomenon conservation equations, since this method keeps the conservative property of the equations and its physical consistency in the numerical process. A nonstaggered grid was employed, and all dependent variables are evaluated at the cell center points, which divides the physical domain. The convection-diffusion fluxes at the control volumes faces are evaluated with the Power Law and Quick shemes. Special attention is paid to the numerical treatment of boundary conditions. The problem of velocity-pressure-density coupling is solved using a combination of continuity, momentum equations and state equation resulting in two pressure correction equations. The first equation corrects the density and the pressure, the second equation corrects the mass flux and the velocity. A modification in the velocity correction equations is proposed using a compensationterm to accelerate the convergence. Several types of interpolation of the face density are used to reduce variable atenuations, caused by false diffusion. For the solution of the resulting algebric equations,the line-by-line TDMA algorith is used as well as a block-correction method to accelerate the convergence. The proposed method is verified on six test problems,by comparing the present results with analytical and numerical results avaiable in the literature.

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31

Hendriana, Dena. "A parabolic quadrilateral finite element for compressible and incompressible flows." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50060.

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Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998. Includes bibliographical references (leaves 156-161). A unified finite element solution scheme for incompressible and compressible flows would be most attractive in engineering practice. The objective in this thesis was to work toward this goal. A 9-node finite element for compressible and incompressible 2-D flow solutions is presented. In the compressible flow formulation, a new high-order derivative artificial diffusion and a new shock capturing term are employed to stabilize the formulation. The new upwinding term is shown numerically to stabilize the formulation and an inf-sup test is performed assuming idealized 1-D conditions. The new shock capturing term performed well in the solutions of various judiciously selected numerical examples. Various flow problems in which the Mach numbers range from about 0.0005 to 6 are considered. The numerical results indicate that the element is applicable to a wide range of analysis problems. For incompressible flows, the element must satisfy the relevant inf-sup condition, and an element is used with parabolic velocity and linear pressure interpolations (the 9/4c-element). An upwinding term in a similar form as for the compressible flow solution is introduced to stabilize the formulation. A convergence study with the formulation to estimate the order of convergence is performed. In addition, a new low order element is presented. The new solution schemes for compressible and incompressible flows provide effective solution techniques and the study provides insight into the difficulties encountered in the development of a unified scheme for incompressible and compressible flows. by Dena Hendriana. Sc.D.

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32

Lin, Chi-Kun. "On the incompressible limit of the compressible Navier-Stokes equations." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185888.

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Many interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.

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33

Fu, Yun. "Linear stability of an interface between two incompressible fluids." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1142955745.

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34

Niederhaus, Charles Edward. "Experiments on the Richtmyer-Meshkov instability of incompressible fluids." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/284290.

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Richtmyer-Meshkov (R-M) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes perturbations on the interface to grow and to possibly become turbulent. R-M instability is a fundamental fluid instability that is important to fields ranging from astrophysics to high-speed combustion. For example, R-M instability is currently one of the limiting factors in achieving a positive net yield in laser driven inertial confinement fusion experiments. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. After undergoing a nearly impulsive acceleration, the initial perturbation quickly inverts and then grows in amplitude. The vorticity on the interface eventually coalesces into a series of alternating signed vortices. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial perturbation growth rates, while the predicted amplitudes differ by less than 10% from experimental measurements up to a nondimensional time kȧ₀t = 0.7. Fourth order, single-mode perturbation theory extends the 1.0% amplitude agreement up to a nondimensional time kȧ₀t = 1.3. A discrete vortex model and a combined model equation are within 10% of the experimental amplitude measurements up to the maximum experimental nondimensional time kȧ₀t = 30. The effects of Reynolds number (based on circulation) on the vortex core evolution and overall growth rate of the interface are also investigated. In addition, an instability in the vortex cores is observed for the first time and criteria established for its occurrence.

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35

Batty, Christopher. "Simulating viscous incompressible fluids with embedded boundary finite difference methods." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/28642.

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The behaviour of liquids and gases ranks among the most familiar and yet complex physical phenomena commonly encountered in daily life. To create a seamless approximation of the real world, it is clear that we must be able to accurately simulate fluids. However, a crucial element of what makes fluid behaviour so complex and compelling is its interactions with its surroundings. To simulate the motion of a fluid we cannot consider the Navier-Stokes equations in isolation; we must also examine the boundary conditions at the point where the fluid meets the world. Enforcing these boundary conditions has traditionally been a source of tremendous difficulty. Cartesian grid-based methods typically approximate the world in an unrealistic, axis-aligned block representation, while conforming mesh methods frequently suffer from poor mesh quality and expensive mesh generation. This thesis examines the use of embedded boundary finite difference methods to alleviate these shortcomings by providing a degree of sub-grid information that enables more efficient, flexible, accurate, and realistic simulations. The first key contribution of the thesis is the use of a variational approach to derive novel embedded boundary finite difference methods for fluids, by exploiting the concept of natural boundary conditions. This idea is applied first to animate the interaction between incompressible fluids and irregularly shaped dynamic rigid bodies. I then apply a similar technique to properly handle viscous free surfaces, enabling realistic buckling and coiling in viscous flows. Lastly, I unify these ideas to simulate Stokes flows in the presence of both free surface and solid boundaries, and demonstrate the method's convergence on a range of examples. The second main contribution is a study of embedded boundary methods for pressure projection in the context of unstructured Delaunay and Voronoi meshes. By eliminating the need for boundary-conforming meshes, this work enables efficient high-quality adaptive mesh generation and improves simulation accuracy. Furthermore, it demonstrates that by placing simulation samples at Voronoi sites, and choosing these sites intelligently with respect to liquid geometry, one can eliminate surface noise, improve the realism and stability of surface tension, and plausibly simulate nearly arbitrarily thin sheets and droplets.

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36

Denk, Kerem. "Development Of A Pressure-based Solver For Both Incompressible And Compressible Flows." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609100/index.pdf.

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The aim of this study is to develop a two-dimensional pressure-based Navier-Stokes solver for incompressible/compressible flows. Main variables are Cartesian velocity components, pressure and temperature while density is linked to pressure via equation of state. Modified SIMPLE algorithm is used to achieve pressure-velocity coupling. Finite Volume discretisation is performed on non-orthogonal and boundary-fitted grids. Collocated variable arrangement is preferred because of its advantage on staggered arrangement in non-orthogonal meshes. Face velocities are calculated using Rhie-Chow momentum interpolation scheme to avoid pressure checkerboarding effect. The solver is validated by solving a number of benchmark problems.

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MacKay, Alexander. "Theoretical and computational modelling of compressible and nonisothermal viscoelastic fluids." Thesis, Cardiff University, 2018. http://orca.cf.ac.uk/118620/.

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This thesis is an investigation into the modelling of compressible viscoelastic fluids. It can be divided into two parts: (i) the development of continuum models for compressible and nonisothermal viscoelastic fluids using the generalised bracket method and (ii) the numerical modelling of compressible viscoelastic flows using a stabilised finite element method. We introduce the generalised bracket method, a mathematical framework for deriving systems of transport equations for viscoelastic fluids based on an energy/entropy formulation. We then derive nonisothermal and compressible generalisations of the Oldroyd-B, Giesekus and FENE-P constitutive equations. The Mackay-Phillips (MP) class of dissipative models for Boger fluids is developed within the bracket framework, complimenting the class of phenomenological models that already exist in the literature. Advantages of the MP models are their generality and consistency with the laws of thermodynamics. A Taylor-Galerkin finite element scheme is used as a basis for numerical simulations of compressible and nonisothermal viscoelastic flow. Numerical predictions for four 2D benchmark problems: lid-driven cavity flow, natural convection, eccentric Taylor-Couette flow and axisymmetric flow past a sphere are presented. In each case numerical comparisons with both empirical and numerical data from the literature are presented and discussed. Numerical drag predictions for the FENE-P-MP model are presented, displaying good agreement with both numerical and experimental data for the drag behaviour of Boger fluids.

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Brezina, Jan. "Selected mathematical problems in the thermodynamics of viscous compressible fluids." Toulon, 2008. http://tel.archives-ouvertes.fr/tel-00443927/fr/.

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We present a complete existence theory for the physical system consisting of a viscous compressible fluid and a number of rigid bodies in it. We assume a bounded domain and homogeneous Dirichlet boundary conditions for the velocity. Both the fluid and the bodies are allowed to be heat-conducting and share the heat. The existence of global-in-time variational solutions is proved via the viscosity penalization method due to San Martin, Starovoitov, Tucsnak, whereas the existence theory for a viscous compressible fluid developed by Feireisl is used in the approximations as well as in the last high-viscosity limit. The second subject is an improvement of the existence theory for steady barotropic ows. We use L1 estimates for the inverse Laplacian of the pressure introduced by Plotnikov,Sokolowski and Frehse, Goj, Steinhauer together with the non-linear potential theory due to Adams and Hedberg, to get a priori estimates and to prove existence of weak solutions Nous présentons une théorie d'existence complète pour le système physique composé de fluides visqueux et des corps rigides plongés dedans. Nous considérons un domaine borné et les conditions aux limites de Dirichlet homogènes pour la vélocité. Le fluide et les corps sont conducteurs thermiques et ils échangent la chaleur. L'existence de la solution variationnelle globale dans le temps est démontrée par la méthode de pénalisation par la viscosité due à Conca, San Martin et Tucsnak. Dans les approximations ainsi que dans la dernière limite nous employons la théorie d'existence pour un fluide visqueux compressible développé par Feireisl. Le deuxième sujet est une amélioration dans la théorie d'existence pour un écoulement barotropique stationnaire. Nous utilisons les estimations potentielles pour la pression proposées par Plotnikov, Sokolowski, Frehse, Goj et Steinhauer. En utilisant ces estimations avec la théorie potentielle non-linéaire nous en concluons les estimations à priori et nous prouvons l'existence des solutions faibles

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Rezzolla, Luciano. "General relativistic hydrodynamics of compressible multicomponent fluids: developments and applications." Doctoral thesis, SISSA, 1997. http://hdl.handle.net/20.500.11767/3985.

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Chien, Ssu-Ying. "Compressible Lubrication Theory in Pressurized Gases." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/88868.

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Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without effective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional effects, unsteadiness, turbulence, variable material properties, non-newtonian fluids, multi-phase flows, wall slip, and thermal effects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working fluids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse effects due to fouling, and compatibility with power system working fluids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-fitting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses five problems involving our new Reynolds equation. In the first, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the "effective bulk modulus". The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplified formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically three-dimensional flows. A finite difference scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed flows. This Reynolds equation is then solved using perturbation methods for high-speed flows. It is found that the flow structure is comprised of five boundary layer regions in addition to the main ``core'' region. The flow in two of these boundary layer regions is governed by a nonlinear heat equation and the flow in three of these boundary layers is governed by nonlinear relaxation equations. Finite difference schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the flow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical flows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the first detailed discussions of the physics of lubrication in dense and supercritical flows, and the discovery of boundary layer structures in flows associated with thrust bearings. Doctor of Philosophy Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without eective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional eects, unsteadiness, turbulence, variable material properties, non-newtonian uids, multi-phase ows, wall slip, and thermal eects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working uids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse eects due to fouling, and compatibility with power system working uids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-tting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses ve problems involving our new Reynolds equation. In the rst, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the eective bulk modulus. The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplied formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically threedimensional ows. A nite dierence scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed ows. This Reynolds equation is then solved using perturbation methods for high-speed ows. It is found that the ow structure is comprised of ve boundary layer regions in addition to the main core region. The ow in two of these boundary layer regions is governed by a nonlinear heat equation and the ow in three of these boundary layers is governed by nonlinear relaxation equations. Finite dierence schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the ow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical ows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the rst detailed discussions of the physics of lubrication in dense and supercritical ows, and the discovery of boundary layer structures in ows associated with thrust bearings.

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41

Peterson, Richard. "The numerical solution of free surface problems for incompressible Newtonian fluids." Thesis, University of Leeds, 2000. http://etheses.whiterose.ac.uk/1288/.

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This thesis describes a new approach for the solution of two-dimensional, time-dependent, surface-tension-driven free-surface flows involving domains of arbitrary shape that may undergo large changes in shape during the course of a problem. Both Stokes and Navier-Stokes problems are considered, a mixed Lagrangian-Eulerian finite element formulation being employed for the latter. All meshes are generated automatically using a Delaunay mesh generator, the onnly user input required being the specification of the initial free-surface shape. Very few constraints are placed on the shape of the initial domain and arbitrarily large deformations of the domain are permitted. A key feature of the new method is its ability to dynamically refine and de-refine the free-surface discretisation as and when necessary to maintain an accurate representation of the free surface, as is essential for surface-tension-driven problems. Full implementation details are included. Semi-implicit time integration schemes are employed for both Stokes and Navier-Stokes problems, the resulting systems of linear equations being solved by the conjugate residual method preconditioned using high-quality, thresholded, incomplete LU factorisations. A novel scheme for the automatic selection of the maximum time step size that ensures free-surface stability is described. A number of challenging problems are considered. First a Stokes-flow problem with a known analytic solution is employed to confirm that the expected rates of convergence in the solution are obtained. Next the Stokes-flow evolution of a film of viscous fluid on a rotating cylinder is investigated, the time-dependent case being modelled for the first time. Illustrations of the large free-surface deformations leading up to load shedding are presented. In addition, the unexpected existence of apparently stable oscillatory solutions is reported for certain configurations. Finally the axisymmetric oscillations of droplets at low Reynolds numbers (Re < 100) are considered.

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42

Fambri, Francesco. "Discontinuous Galerkin methods for compressible and incompressible flows on space-time adaptive meshes." Doctoral thesis, Università degli studi di Trento, 2017. https://hdl.handle.net/11572/368742.

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In this work the numerical discretization of the partial differential governing equations for compressible and incompressible flows is dealt within the discontinuous Galerkin (DG) framework along space-time adaptive meshes. Two main research fields can be distinguished: (1) fully explicit DG methods on collocated grids and (2) semi-implicit DG methods on edge-based staggered grids. DG methods became increasingly popular in the last twenty years mainly because of three intriguing properties: i) non-linear L2 stability has been proven; ii) arbitrary high order of accuracy can be achieved by simply increasing the polynomial order of the chosen basis functions, used for approximating the state-variables; iii) high scalability properties make DG methods suitable for large-scale simulations on general unstructured meshes. It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called â€™Gibbs phenomenonâ€™. Over the years, several attempts have been made to cope with this problem and different kinds of limiters have been proposed. Among them, a rather intriguing paradigm has been defined in the work of [71], in which the nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a multidimensional optimal order detection (MOOD) criterion. In the present work the main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection criteria is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Then, in those cells where at least one of these criteria is violated the computed candidate solution is detected as troubled and is locally rejected. Next, the numerical solution of the previous time step is scattered onto cell averages on a suitable sub-grid in order to preserve the natural sub-cell resolution of the DG scheme. Then, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume scheme on the sub-grid averages within that troubled cell. Finally, a high order DG polynomial is reconstructed back from the evolved sub-cell averages. Moreover, handling typical multiscale problems, dynamic adaptive mesh refinement (AMR) and adaptive polynomial order methods are probably the two main ways of preserving accuracy and efficiency, and saving computational effort. The here adopted AMRapproach is the so called â€™cell by cellâ€™ refinement because of its formally very simple tree-type data structure. In the here-presented â€™cell-by-cellâ€™ AMR every single element is recursively refined, from a coarsest refinement level l0 = 0 to a prescribed finest (maximum) refinement level lmax, accordingly to a refinement-estimator function X that drives step by step the choice for recoarsening or refinement. The combination of the sub-cell resolution with the advantages of AMR allows for an unprecedented ability in resolving even the finest details in the dynamics of the fluid. First, the Euler equations of compressible gas dynamics and the magnetohydrodynamics (MHD) equations have been treated [281]. Then, the presented method has been readily extended to the special relativistic ideal MHD equations [280], but also the the case of diffusive fluids, i.e. fluid flows in the presence of viscosity, thermal conductivity and magnetic resistivity [116]. In particular, the adopted formalism is quite general, leading to a novel family of adaptive ADER-DG schemes suitable for hyperbolic systems of partial differential equations in which the numerical fluxes also depend on the gradient of the state vector because of the parabolic nature of diffusive terms. The presented results show clearly that the shock-capturing capability of the news schemes are significantly enhanced within the cell-by-cell Adaptive Mesh Refinement (AMR) implementation together with time accurate local time stepping (LTS). The resolution properties of the new scheme have been shown through a wide number of test cases performed in two and in three space dimensions, from low to high Mach numbers, from low to high Reynolds regimes. In particular, concerning MHD equations, the divergence-free character of the magnetic field is taken into account through the so-called hyperbolic â€™divergence-cleaningâ€™ approach which allows to artificially transport and spread the numerical spurious â€™magnetic monopolesâ€™ out of the computational domain. A special treatment has been followed for the incompressible Navier-Stokes equations. In fact, the elliptic character of the incompressible Navier-Stokes equations introduces an important difficulty in their numerical solution: whenever the smallest physical or numerical perturbation arises in the fluid flow then it will instantaneously affect the entire computational domain. Thus, a semi-implicit approach has been used. The main advantage of making use of a semi-implicit discretization is that the numerical stability can be obtained for large time-steps without leading to an excessive computational demand [117]. In this context, we derived two new families of spectral semi-implicit and spectral space-time DG methods for the solution of the two and three dimensional Navier-Stokes equations on edge-based staggered Cartesian grids [115], following the ideas outlined in [97] for the shallow water equations. The discrete solutions of pressure and velocity are expressed in the form of piecewise polynomials along different meshes. While the pressure is defined on the control volumes of the main grid, the velocity components are defined on edge-based dual control volumes, leading to a spatially staggered mesh. In the first family, high order of accuracy is achieved only in space, while a simple semi-implicit time discretization is derived by introducing an implicitness factor theta in [0.5, 1] for the pressure gradient in the momentum equation. The real advantages of the staggering arise after substituting the discrete momentum equation into the weak form of the continuity equation. In fact, the resulting linear system for the pressure is symmetric and positive definite and either block penta-diagonal (in 2D) or block hepta-diagonal (in 3D). As a consequence, the pressure system can be solved very efficiently by means of a classical matrix-free conjugate gradient method. Moreover, a rigorous theoretical analysis of the condition number of the resulting linear systems and the design of specific preconditioners, using the theory of matrix-valued symbols and Generalized Locally Toeplitz (GLT) algebra has been successfully carried out with promising results in terms of numerical efficiency [102]. The resulting algorithm is stable, computationally very efficient, and at the same time arbitrary high order accurate in both space and time. The new numerical method has been thoroughly validated for approximation polynomials of degree up to N = 11, using a large set of non-trivial test problems in two and three space dimensions, for which either analytical, numerical or experimental reference solutions exist. Moreover, the here mentioned semi-implicit DG method has been successfully extended to a novel edge-based staggered â€™cell-by-cellâ€™ adaptive meshes [114].

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43

Fambri, Francesco. "Discontinuous Galerkin methods for compressible and incompressible flows on space-time adaptive meshes." Doctoral thesis, University of Trento, 2017. http://eprints-phd.biblio.unitn.it/2048/1/PhD_FrancescoFambri_January2017.pdf.

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Abstract:

In this work the numerical discretization of the partial differential governing equations for compressible and incompressible flows is dealt within the discontinuous Galerkin (DG) framework along space-time adaptive meshes. Two main research fields can be distinguished: (1) fully explicit DG methods on collocated grids and (2) semi-implicit DG methods on edge-based staggered grids. DG methods became increasingly popular in the last twenty years mainly because of three intriguing properties: i) non-linear L2 stability has been proven; ii) arbitrary high order of accuracy can be achieved by simply increasing the polynomial order of the chosen basis functions, used for approximating the state-variables; iii) high scalability properties make DG methods suitable for large-scale simulations on general unstructured meshes. It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called ’Gibbs phenomenon’. Over the years, several attempts have been made to cope with this problem and different kinds of limiters have been proposed. Among them, a rather intriguing paradigm has been defined in the work of [71], in which the nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a multidimensional optimal order detection (MOOD) criterion. In the present work the main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection criteria is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Then, in those cells where at least one of these criteria is violated the computed candidate solution is detected as troubled and is locally rejected. Next, the numerical solution of the previous time step is scattered onto cell averages on a suitable sub-grid in order to preserve the natural sub-cell resolution of the DG scheme. Then, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume scheme on the sub-grid averages within that troubled cell. Finally, a high order DG polynomial is reconstructed back from the evolved sub-cell averages. Moreover, handling typical multiscale problems, dynamic adaptive mesh refinement (AMR) and adaptive polynomial order methods are probably the two main ways of preserving accuracy and efficiency, and saving computational effort. The here adopted AMRapproach is the so called ’cell by cell’ refinement because of its formally very simple tree-type data structure. In the here-presented ’cell-by-cell’ AMR every single element is recursively refined, from a coarsest refinement level l0 = 0 to a prescribed finest (maximum) refinement level lmax, accordingly to a refinement-estimator function X that drives step by step the choice for recoarsening or refinement. The combination of the sub-cell resolution with the advantages of AMR allows for an unprecedented ability in resolving even the finest details in the dynamics of the fluid. First, the Euler equations of compressible gas dynamics and the magnetohydrodynamics (MHD) equations have been treated [281]. Then, the presented method has been readily extended to the special relativistic ideal MHD equations [280], but also the the case of diffusive fluids, i.e. fluid flows in the presence of viscosity, thermal conductivity and magnetic resistivity [116]. In particular, the adopted formalism is quite general, leading to a novel family of adaptive ADER-DG schemes suitable for hyperbolic systems of partial differential equations in which the numerical fluxes also depend on the gradient of the state vector because of the parabolic nature of diffusive terms. The presented results show clearly that the shock-capturing capability of the news schemes are significantly enhanced within the cell-by-cell Adaptive Mesh Refinement (AMR) implementation together with time accurate local time stepping (LTS). The resolution properties of the new scheme have been shown through a wide number of test cases performed in two and in three space dimensions, from low to high Mach numbers, from low to high Reynolds regimes. In particular, concerning MHD equations, the divergence-free character of the magnetic field is taken into account through the so-called hyperbolic ’divergence-cleaning’ approach which allows to artificially transport and spread the numerical spurious ’magnetic monopoles’ out of the computational domain. A special treatment has been followed for the incompressible Navier-Stokes equations. In fact, the elliptic character of the incompressible Navier-Stokes equations introduces an important difficulty in their numerical solution: whenever the smallest physical or numerical perturbation arises in the fluid flow then it will instantaneously affect the entire computational domain. Thus, a semi-implicit approach has been used. The main advantage of making use of a semi-implicit discretization is that the numerical stability can be obtained for large time-steps without leading to an excessive computational demand [117]. In this context, we derived two new families of spectral semi-implicit and spectral space-time DG methods for the solution of the two and three dimensional Navier-Stokes equations on edge-based staggered Cartesian grids [115], following the ideas outlined in [97] for the shallow water equations. The discrete solutions of pressure and velocity are expressed in the form of piecewise polynomials along different meshes. While the pressure is defined on the control volumes of the main grid, the velocity components are defined on edge-based dual control volumes, leading to a spatially staggered mesh. In the first family, high order of accuracy is achieved only in space, while a simple semi-implicit time discretization is derived by introducing an implicitness factor theta in [0.5, 1] for the pressure gradient in the momentum equation. The real advantages of the staggering arise after substituting the discrete momentum equation into the weak form of the continuity equation. In fact, the resulting linear system for the pressure is symmetric and positive definite and either block penta-diagonal (in 2D) or block hepta-diagonal (in 3D). As a consequence, the pressure system can be solved very efficiently by means of a classical matrix-free conjugate gradient method. Moreover, a rigorous theoretical analysis of the condition number of the resulting linear systems and the design of specific preconditioners, using the theory of matrix-valued symbols and Generalized Locally Toeplitz (GLT) algebra has been successfully carried out with promising results in terms of numerical efficiency [102]. The resulting algorithm is stable, computationally very efficient, and at the same time arbitrary high order accurate in both space and time. The new numerical method has been thoroughly validated for approximation polynomials of degree up to N = 11, using a large set of non-trivial test problems in two and three space dimensions, for which either analytical, numerical or experimental reference solutions exist. Moreover, the here mentioned semi-implicit DG method has been successfully extended to a novel edge-based staggered ’cell-by-cell’ adaptive meshes [114].

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44

Mrabet, Ahmed Amine. "Accélérations algorithmiques pour la simulation numérique d’impacts de vagues. Modèles de type "roofline" pour la caractérisation des performances, application à la CFD." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLN010/document.

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Au cours de ces dernières années les processeurs sont devenus de plus en plus complexes (plusieurs niveaux de cache, vectorisation,...), l’augmentation de la complexité fait que l’étude des performances et les optimisations sont eux aussi devenus de plus en plus complexes et difficiles à comprendre. Donc développer un outil de caractérisation simple et facile d’utilisation des performances d’applications, serait de grande valeur. Le Modèle Roofline [17] promet un début de réponse à ces critères, mais reste insuffisant pour une caractérisation robuste et détaillée. Dans la première partie de cette thèse, Nous allons développer plusieurs versions améliorées du Roofline, robustes et précises, en passant par une version du Roofline en fonction du temps, des blocs et enfin la nouvelle version du Roofline introduite dans la suite de caractérisation Vtune d’Intel. Pour valider ces modèles, nous utilisons le benchmark LINPACK, STREAM ainsi qu’une mini-application développée au cours de cette thèse, qui résout l’équation de l’advection et qui servira de prototype pour l’évaluation de codes hydrodynamiques explicites. Nous portons aussi cette mini-application sur les co-processeurs d’Intel Xeon Phi KNL et KNC. Dans la deuxième partie de cette thèse nous nous intéressons à la simulation d’impact de vagues, à l’aide de codes industriels compressibles et incompressibles. Nous rajoutons plusieurs fonctionnalités dans le code compressible FluxIC, nous effectuons un chaînage de codes incompressible et compressible et enfin nous introduisons un nouveau schéma numérique appelé liquide incompressible et gaz quasi-compressible, qui permet de réaliser une simulation d’impact d’une vague via un code incompressible avec une correction compressible dans les zones où la compressibilité du gaz est importante During recent years computer processors have become increasingly complex (multiple levels of cache, vectorization, etc), meaning that the study of performance and optimization is also becoming more complex and difficult to understand. So a simple and easy-to-use model aimed at studying the performance of applications would be of great value. The Roofline model [17] promises to meet this criteria, but it is insufficient for robust and detailed characterization.In the first part of this thesis, several improved versions of the Roofline model, that are more robust and accurate, are developed by going through theRoofline version as a function of time and block, and finally a new Rooflinemodel is implemented in the Intel Vtune characterization suite. To validate thenew models, the LINPACK andtextitSTREAM benchmarks are used, as wellas, a mini-application developed during this thesis that solves the advectionequation and serves as a prototype for the evaluation of explicit hydrodynamicsimulation codes. This mini-application is also ported to the new Intel XeonPhi KNL and KNC co-processors.Simulation of wave impact using compressible and incompressible industrialcodes is the focus of the second part of this thesis. Several functionalities are added to the compressible FluxIC code, and a chaining of compressible andincompressible codes is carried out. Finally, a new numerical scheme called"incompressible liquid and quasi-compressible gas" is introduced, which allowsthe simulation of wave impact using an incompressible code with a compressiblecorrection in areas where gas compressibility is significant

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45

HUITRIC, JACQUES. "Contribution à l'étude des joints d'étanchéité à faces radiales rainurées, en présence de fluides compressibles ou incompressibles : analyse par éléments finis." Poitiers, 1993. http://www.theses.fr/1993POIT2280.

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Les joints d'etancheite a faces radiales rainurees constituent un element essentiel de l'etancheite dynamique dans les mecanismes tournants. Leur emploi s'est recemment generalise dans le cas des gaz, mais il n'existe encore que peu d'etudes a leur sujet. Les brusques variations d'epaisseur du film, au niveau des rainures, introduisent des discontinuites qui rendent difficile la resolution de l'equation de reynolds. De plus, lorsque le fluide est compressible, il est necessaire d'introduire l'equation d'etat des gaz; l'equation de reynolds devient alors non lineaire. Par contre, dans le cas des fluides incompressibles, la rupture du film lubrifiant introduit une frontiere inconnue, on doit alors resoudre un probleme a frontiere libre. L'etude de ces problemes nous a conduit a developper un logiciel aux elements finis dont la validation a ete effectuee par comparaison avec des resultats experimentaux et theoriques simples existants par ailleurs. L'optimisation d'une garniture a gaz comportant 12 rainures spirales a ete ensuite realisee en analysant l'effet de la profondeur, de la largeur et du rayon de fin de rainures sur les performances du joint. Enfin, l'etude d'un joint comportant des ondulations pouvant etre induites par l'effet conjugue de la temperature et des rainures a ete effectuee; dans le cas de faces alignees, l'effet hydrostatique, est preponderant par rapport a l'effet hydrodynamique

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46

Pattinson, John. "A cut-cell, agglomerated-multigrid accelerated, Cartesian mesh method for compressible and incompressible flow." Pretoria : [s.n.]m, 2006. http://upetd.up.ac.za/thesis/available/etd-07052007-103047.

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47

Shu, Yupeng. "Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian Fluids." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2051.

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The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

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48

Wang, Jin. "A numerical approach for the interfacial motion between two immiscible incompressible fluids." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1092675815.

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Thesis (Ph. D.)--Ohio State University, 2004. Title from first page of PDF file. Document formatted into pages; contains xiii, 152 p.; also includes graphics. Includes bibliographical references (p. 147-152).

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49

Boulakia, Muriel. "Modélisation et analyse mathématique de problèmes d'interaction fluide-structure." Phd thesis, Université de Versailles-Saint Quentin en Yvelines, 2004. http://tel.archives-ouvertes.fr/tel-00008138.

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Cette thèse traite des problèmes d'interaction fluide-structure. Deux familles de problèmes sont présentées : l'interaction entre une structure élastique et un fluide incompressible et l'interaction entre une structure élastique et un fluide compressible. La structure est immergée dans le fluide et l'ensemble évolue dans une cavité fixe bornée. Le mouvement du solide se compose d'un mouvement rigide (translation et rotation) et d'un mouvement élastique. Dans l'équation du mouvement solide, on ajoute un terme qui régularise la déformation élastique. Après avoir justifié le modèle étudié, on montre des résultats d'existence de solutions faibles définies tant qu'il n'y a pas de chocs entre la structure et la paroi de la cavité et tant que des conditions de non-interpénétration et de préservation de l'orientation du solide sont satisfaites.

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50

Tegegn, Tesfalem Abate. "Magnetohydrodynamic turbulent flows for viscous incompressible fluids through the lenses of harmonic analysis." Thesis, University of Pretoria, 2016. http://hdl.handle.net/2263/60865.

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This thesis is divided into three main parts devoted to the study of magnetohydrodynamics (MHD) turbulence flows. Part I consists of introduction and background (or preliminary) materials which were crucially important in the process. The main body of the thesis is included in parts II and III. In Part II, new regularity results for stochastic heat equations in probabilistic evolution spaces of Besov type are established, which in turn were used to establish global and local in time existence and uniqueness results for stochastic MHD equations. The existence result holds with positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools, such as Littlewood-Paley decomposition, Jean-Micheal Bony paradifferential calculus and stochastic calculus. Our global existence result is new in three-dimensional spaces and is published in [148](Sango and Tegegn, Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces, International Journal of Modern Physics B, World Scientific, 2016, 30). Our results in this part are novel; they introduced Littlewood-Paley theory and paradifferential calculus for stochastic partial differential equation. In Part III, we studied Kolmogorov's spectral theory for MHD equations with reasonably smooth external forces applied to both velocity and magnetic fields. Thesis (PhD)--University of Pretoria, 2016. Mathematics and Applied Mathematics PhD Unrestricted

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