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Dogan, Abdulkadir. "Petrov-Galerkin finite element methods." Thesis, Bangor University, 1997. https://research.bangor.ac.uk/portal/en/theses/petrovgalerkin-finite-element-methods(4d767fc7-4ad1-402a-9e6e-fd440b722406).html.
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Hellwig, Friederike. "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20034.
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Die vorliegende Arbeit "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods" beweist optimale Konvergenzraten für vier diskontinuierliche Petrov-Galerkin (dPG) Finite-Elemente-Methoden für das Poisson-Modell-Problem für genügend feine Anfangstriangulierung. Sie zeigt dazu die Äquivalenz dieser vier Methoden zu zwei anderen Klassen von Methoden, den reduzierten gemischten Methoden und den verallgemeinerten Least-Squares-Methoden. Die erste Klasse benutzt ein gemischtes System aus konformen Courant- und nichtkonformen Crouzeix-Raviart-Finite-Elemente-Funktionen. Die zweite Klasse verallgemeinert die Standard-Least-Squares-Methoden durch eine Mittelpunktsquadratur und Gewichtsfunktionen.
Diese Arbeit verallgemeinert ein Resultat aus [Carstensen, Bringmann, Hellwig, Wriggers 2018], indem die vier dPG-Methoden simultan als Spezialfälle dieser zwei Klassen charakterisiert werden. Sie entwickelt alternative Fehlerschätzer für beide Methoden und beweist deren Zuverlässigkeit und Effizienz.
Ein Hauptresultat der Arbeit ist der Beweis optimaler Konvergenzraten der adaptiven Methoden durch Beweis der Axiome aus [Carstensen, Feischl, Page, Praetorius 2014]. Daraus folgen dann insbesondere die optimalen Konvergenzraten der vier dPG-Methoden.
Numerische Experimente bestätigen diese optimalen Konvergenzraten für beide Klassen von Methoden. Außerdem ergänzen sie die Theorie durch ausführliche Vergleiche beider Methoden untereinander und mit den äquivalenten dPG-Methoden.The thesis "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods" proves optimal convergence rates for four lowest-order discontinuous Petrov-Galerkin methods for the Poisson model problem for a sufficiently small initial mesh-size in two different ways by equivalences to two other non-standard classes of finite element methods, the reduced mixed and the weighted Least-Squares method. The first is a mixed system of equations with first-order conforming Courant and nonconforming Crouzeix-Raviart functions. The second is a generalized Least-Squares formulation with a midpoint quadrature rule and weight functions. The thesis generalizes a result on the primal discontinuous Petrov-Galerkin method from [Carstensen, Bringmann, Hellwig, Wriggers 2018] and characterizes all four discontinuous Petrov-Galerkin methods simultaneously as particular instances of these methods. It establishes alternative reliable and efficient error estimators for both methods. A main accomplishment of this thesis is the proof of optimal convergence rates of the adaptive schemes in the axiomatic framework [Carstensen, Feischl, Page, Praetorius 2014]. The optimal convergence rates of the four discontinuous Petrov-Galerkin methods then follow as special cases from this rate-optimality. Numerical experiments verify the optimal convergence rates of both types of methods for different choices of parameters. Moreover, they complement the theory by a thorough comparison of both methods among each other and with their equivalent discontinuous Petrov-Galerkin schemes.
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Herron, Madonna Geradine. "A novel approach to image derivative approximation using finite element methods." Thesis, University of Ulster, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364539.
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Bonhaus, Daryl Lawrence. "A Higher Order Accurate Finite Element Method for Viscous Compressible Flows." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/29458.
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The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order
finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes
equations in two dimensions. The unknown flow quantities are discretized on
meshes of triangular elements using triangular Bezier patches. The nonlinear residual
equations are solved using an approximate Newton method with a pseudotime term. The
resulting linear system is solved using the Generalized Minimum Residual algorithm with
block diagonal preconditioning.
The exact solutions of Ringleb flow and Couette flow are used to quantitatively
establish the spatial convergence rate of each discretization. Examples of inviscid flows
including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows
past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past
a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretiza-tions.
The scheme achieves higher order accuracy without modification. Based on the test
cases presented, significant improvement of the solution can be expected using the higher-order
schemes with little or no increase in computational requirements. The nonlinear sys-tem
also converges at a higher rate as the order of accuracy is increased for the same num-ber
of degrees of freedom; however, the linear system becomes more difficult to solve.
Several avenues of future research based on the results of the study are identified, includ-ing
improvement of the SU/PG formulation, development of more general grid generation
strategies for higher order elements, the addition of a turbulence model to extend the
method to high Reynolds number flows, and extension of the method to three-dimensional
flows. An appendix is included in which the method is applied to inviscid flows in three
dimensions. The three-dimensional results are preliminary but consistent with the findings
based on the two-dimensional scheme.Ph. D.
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Wu, Wei. "Petrov-Galerkin methods for parabolic convection-diffusion problems." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670384.
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Sampaio, Paulo Angusto Berquo de. "Petrov-Galerkin finite element formulations for incompressible viscous flows." Thesis, Swansea University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638759.
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The basic difficulties associated with the numerical solution of the incompressible Navier-Stokes equations in primitive variables are identified and analysed. These difficulties, namely the lack of self-adjointness of the flow equations and the requirement of choosing compatible interpolations for velocity and pressure, are addressed with the development of consistent Petrov-Galerkin formulations. In particular, the solution of incompressible viscous flow problems using simple equal order interpolation for all variables becomes possible.
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Scotney, Bryan. "An analysis of the Petrov-Galerkin finite element method." Thesis, University of Reading, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.354097.
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Moro-Ludeña, David. "A Hybridized Discontinuous Petrov-Galerkin scheme for compressible flows." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67189.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 113-117).
The Hybridized Discontinuous Petrov-Galerkin scheme (HDPG) for compressible flows is presented. The HDPG method stems from a combination of the Hybridized Discontinuous Galerkin (HDG) method and the theory of the optimal test functions, suitably modified to enforce the conservativity at the element level. The new scheme maintains the same number of globally coupled degrees of freedom as the HDG method while increasing the stability in the presence of discontinuities or under-resolved features. The new scheme has been successfully tested in several problems involving shocks such as Burgers equation and the Navier-Stokes equations and delivers solutions with reduced oscillation at the shock. When combined with artificial viscosity, the oscillation can be completely eliminated using one order of magnitude less viscosity than that required by other Finite Element methods. Also, convergence studies in the sequence of meshes proposed by Peterson [49] show that, unlike other DG methods, the HDPG method is capable of breaking the suboptimal k+1/2 rate of convergence for the convective problem and thus achieve optimal k+1 convergence.
by David Moro-Ludeña.
S.M.
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Sampaio, Paulo Augusto Berquó de, and Instituto de Engenharia Nuclear. "Petrov - galerkin finite element formulations for incompressible viscous flows." Instituto de Engenharia Nuclear, 1991. http://carpedien.ien.gov.br:8080/handle/ien/1954.
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The basic difficulties associated with the numerical solution of the incompressible Navier-Stokes equations in primitive variables are identified and analysed. These difficulties, namely the lack of self-adjointness of the flow equations and the requirement of choosing compatible interpolations for velocity and pressure, are addressed with the development of consistent Petrov-Galerkin formulations. In particular, the solution of incompressible viscous flow problems using simple equal order interpolation for all variables becomes possible .
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Gerber, George. "Unsteady pipe-flow using the Petrov-Galerkin finite element method." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/50214.
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Thesis (MScEng)--University of Stellenbosch, 2004.ENGLISH ABSTRACT: Presented here is an Eulerian scheme for solving the unsteady pipe-flow equations. It is called the Characteristic Dissipative Petrov-Galerkin finite element algorithm. It is based on Hicks and Steffler's open-channel finite element algorithm [5]. The algorithm features a highly selective dissipative interface, which damps out spurious oscillations in the pressure field while leaving the rest of the field almost unaffected. The dissipative interface is obtained through upwinding of the test shape functions, which is controlled by the characteristic directions of the flow field at a node. The algorithm can be applied to variable grids, since the dissipative interface is locally controlled. The algorithm was applied to waterhammer problems, which included reservoir, deadend, valve and pump boundary conditions. Satisfactory results were obtained using a simple one-dimensional element with linear shape functions.
AFRIKAANSE OPSOMMING: 'n Euleriese skema word hier beskryf om die onbestendige pypvloei differensiaal vergelykings op te los. Dit word die Karakteristieke Dissiperende Petrov-Galerkin eindige element algoritme genoem. Die algoritme is gebaseer op Hicks en Steffler se oop-kanaal eindige element algoritme [5]. In hierdie algoritme word onrealistiese ossilasies in die drukveld selektief gedissipeer, sonder om die res van die veld te beinvloed. Die dissiperende koppelvlak word verkry deur stroomop weegfunksies, wat beheer word deur die karakteristieke rigtings in die vloeiveld, by 'n node. Die algoritme kan dus gebruik word op veranderbare roosters, omdat die dissiperende koppelvlak lokaal beheer word. Die algoritme was toegepas op waterslag probleme waarvan die grenskondisies reservoirs, entpunte, kleppe en pompe ingesluit het. Bevredigende resultate was verkry vir hierdie probleme, al was die geimplementeerde element een-dimensioneel met lineere vormfunksies.
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Hwang, Eduardo. "Simulação numérica de escoamentos: uma implementação com o método Petrov-Galerkin." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/3/3150/tde-11092008-113640/.
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O método SUPG (\"Streamline Upwind Petrov-Galerkin\") é analisado quanto a sua capacidade de estabilizar oscilações numéricas decorrentes de escoamentos convectivo-difusivos, e de manter a consistência nos resultados. Para esta finalidade, é elaborado um programa computacional como uma implementação algorítmica do método, e simulado o escoamento sobre um cilindro fixo a diferentes números de Reynolds. Ao final, é feita uma revelação sobre a solidez do método. Palavras-chave: escoamento, simulação numérica, método Petrov- Galerkin.The \"Streamline Upwind Petrov-Galerkin\" method (SUPG) is analyzed with regard to its capability to stabilize numerical oscillations caused by convective-diffusive flows, and to maintain consistency in the results. To this aim, a computational program is elaborated as an algorithmic implementation of the method, and simulated the flow around a fixed cylinder at different Reynolds numbers. At the end, a revelation is made on the method\'s robustness. Keywords: flow, numerical simulation, Petrov-Galerkin method.
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YU, CHUNG-CHYI. "FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183930.
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Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.
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Storn, Johannes. "Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20141.
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Aufgrund der fundamentalen Bedeutung partieller Differentialgleichungen zur Beschreibung von Phänomenen in angewandten Wissenschaften ist deren Analyse ein Kerngebiet der Mathematik. Durch Computer lassen sich die Lösungen für eine Vielzahl dieser Gleichungen näherungsweise bestimmen. Die dabei verwendeten numerischen Verfahren sollen auf möglichst exakte Approximationen führen und deren Genauigkeit verifizieren. Die Least-Squares Finite-Elemente-Methode (LSFEM) und die unstetige Petrov-Galerkin (DPG) Methode sind solche Verfahren. Sie werden in dieser Dissertation untersucht.
Der erste Teil der Arbeit untersucht die Genauigkeit der mittels LSFEM berechneten Näherungen. Dazu werden Eigenschaften der zugrundeliegenden Differentialgleichungen mit den Eigenschaften der LSFEM kombiniert. Dies zeigt, dass die Abweichung der berechneten Näherung von der exakten Lösung einem berechenbaren Residuum asymptotisch entspricht. Ferner wird ein Verfahren zu Berechnung einer garantierten oberen Fehlerschranke eingeführt. Während etablierte Fehlerschätzer den Fehler signifikant überschätzt, zeigen numerische Experimente eine äußerst geringe Überschätzung des Fehlers mittels der neuen Fehlerschranke.
Die Analyse der Fehlerschranken für das Stokes-Problem offenbart ein Beziehung der LSFEM und der LBB Konstanten. Diese Konstante ist entscheidend für die Existenz und Stabilität von Lösungen in der Strömungslehre. Der zweite Teil der Arbeit nutzt diese Beziehung und entwickelt ein auf der LSFEM basierendes Verfahren zur numerischen Berechnung der LBB Konstanten.
Der dritte Teil der Arbeit untersucht die DPG Methode. Dabei werden existierende Anwendungen der DPG Methode zusammengefasst und analysiert. Diese Analyse zeigt, dass sich die DPG Methode als eine leicht gestörte LSFEM interpretieren lässt. Diese Interpretation erlaubt die Anwendung der Resultate aus dem ersten Teil der Arbeit und ermöglicht dadurch eine genauere Untersuchung existierender und die Entwicklung neuer DPG Methoden.The analysis of partial differential equations is a core area in mathematics due to the fundamental role of partial differential equations in the description of phenomena in applied sciences. Computers can approximate the solutions to these equations for many problems. They use numerical schemes which should provide good approximations and verify the accuracy. The least-squares finite element method (LSFEM) and the discontinuous Petrov-Galerkin (DPG) method satisfy these requirements. This thesis investigates these two schemes. The first part of this thesis explores the accuracy of solutions to the LSFEM. It combines properties of the underlying partial differential equation with properties of the LSFEM and so proves the asymptotic equality of the error and a computable residual. Moreover, this thesis introduces an novel scheme for the computation of guaranteed upper error bounds. While the established error estimator leads to a significant overestimation of the error, numerical experiments indicate a tiny overestimation with the novel bound. The investigation of error bounds for the Stokes problem visualizes a relation of the LSFEM and the Ladyzhenskaya-Babuška-Brezzi (LBB) constant. This constant is a key in the existence and stability of solution to problems in fluid dynamics. The second part of this thesis utilizes this relation to design a competitive numerical scheme for the computation of the LBB constant. The third part of this thesis investigates the DPG method. It analyses an abstract framework which compiles existing applications of the DPG method. The analysis relates the DPG method with a slightly perturbed LSFEM. Hence, the results from the first part of this thesis extend to the DPG method. This enables a precise investigation of existing and the design of novel DPG schemes.
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Moosavi, Mohammad-Reza. "Méthode combinée volumes finis et meshless local Petrov Galerkin appliquée au calcul de structures." Thesis, Nancy 1, 2008. http://www.theses.fr/2008NAN10080/document.
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Ce travail porte sur le développement d’une nouvelle méthode numérique intitulée « Meshless local Petrov Galerkin (MLPG) combinée à la méthode des volumes finis (MVF) » appliquée au calcul de structures. Elle est basée sur la résolution de la forme faible des équations aux dérivées partielles par une méthode de Petrov Galerkin comme en éléments finis, mais par contre l’approximation du champ de déplacement introduite dans la forme faible ne nécessite pas de maillage. Seul un ensemble de nœuds est réparti dans le domaine et l’approximation du champ de déplacement en un point ne dépend que de la distance de ce point par rapport aux nœuds qui l’entourent et non de l’appartenance à un certain élément fini. Les déformations et les déplacements sont déterminés aux différents nœuds par interpolation locale en utilisant les moindres carrés mobiles (MLS). Les valeurs des déformations aux nœuds sont exprimées en termes de valeurs nodales interpolées indépendamment des déplacements, en imposant simplement la relation déformation déplacement directement par collocation aux points nodaux. La procédure de calcul pour cette méthode est implémentée dans un programme de calcul développé sous MATLAB. Le code obtenu a été validé sur un certain nombre de cas tests par comparaison avec des solutions analytiques de référence et des calculs éléments finis comme ABAQUS. L’ensemble de ces tests a montré un bon comportement de la méthode (environs 0.0001% d’erreurs par rapport à la solution exacte). L’approche est étendue pour l’étude des poutres minces et pour l’analyse dynamique et stabilitéThis work concerns the development of a new numerical method entitled “Meshless Local Petrov- Galerkin (MLPG) combined with the Finite Volumes Method (FVM)” applied to the structural analysis. It is based on the resolution of the weak form of the partial differential equations by a method of Petrov Galerkin as in finite elements, but the approximation of the field of displacement introduced into the weak form does not require grid. The displacements and strains are given with the various nodes by local interpolation by using moving least squares (MLS). The values of the nodal strains are expressed in terms of interpolated nodal values independently of displacements, by simply imposing the strain displacement relationship directly by collocation at the nodal points. The procedure of calculation for this method is implemented in a computer code developed in MATLAB. The developed code was validated on a certain number of test cases by comparison with analytical solutions and finite elements results like ABAQUS. The whole of these tests showed a good behaviour of the method (about 0.0001% of errors in compared to the exact solution). The approach is also extended for the study of the thin beams and the dynamic analysis and stability
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Rajaraman, Prathish Kumar. "Simulation of nanoparticle transport in airways using Petrov-Galerkin finite element methods." Thesis, Montana State University, 2012. http://etd.lib.montana.edu/etd/2012/rajaraman/RajaramanP0512.pdf.
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Nanoparticles with various diameters, i.e. 1 nm â���¤ d â���¤ 150 nm, were studied with respect to their transport and deposition properties in the human airways. A finite element code, written in C++, was developed that solved both the Navier-Stokes and Advection-Diffusion equation monolithically. When modeling nanoparticles, the regular finite element method becomes unstable, and, in order resolve this issue, various stabilization methods were consider including Streamline Upwind, Streamline Upwind Petrov-Galerkin and Galerkin Least Square. In order to validate the various types of stabilization, the stabilized finite element solution was compared to the analytical Graetz solution. The comparison was done by calculation an approximation of the L â������ - error, and the best stabilization method was found to be Galerkin Least Square. Also in this thesis, we found that the Crank-Nicolson time stepping scheme is not the best option for the human airways simulations problem, and this is due to both the complex nature of the geometry and the Crank-Nicolson method lacks the ability to damp out error when the problem is advection dominated. However, using Crank-Nicolson in straight tube geometry with various stabilization methods provides better accuracy than other second-order time stepping schemes, such as BDF-2. The type of stabilization method used when d < 10 nm does matter since Streamline Upwind Petrov-Galerkin introduces higher deposition fraction compared to Galerkin Least Square. This statement is not true when d > 10 nm, since mesh refinement is important at this range. In the human airways simulation, we found that for d = 1 nm the concentration distribution is uniform compared to d = 150 nm , where localized concentration exists. This implies a potential health risk when inhaling nanoparticles because nanoparticles have a very high surface area and the potential for exposure is much greater. The stabilization methods tested in this thesis show promise for modeling nanoparticle transport in the human airways.
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Zengeya, Miles. "Journal bearing optimization and analysis using streamline upwind Petrov-Galerkin finite element method." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/8039.
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A three-dimensional finite element thermo-hydrodynamic lubrication model that couples the Reynolds and energy equations is developed. The model uses the streamline upwind Petrov-Galerkin (SUPG) method. Model results indicate that the peak temperature location in slider bearing is on the mid-plane well as when pressure boundary conditions are altered in such a way that the inlet/outlet pressure is higher than the side pressure. The adiabatic temperature profiles of an infinite and square sliders are compared. The wider slider shows a higher peak temperature. Side flow plays a major role in determining the value and position of the peak temperature. Model results also indicate peak side flow at a width-to-length ratio of 2. A method of optimizing leakage, the Flow Gradient Method, is proposed.
The SUPG finite element method shows rapid convergence for slider and plain journal bearings and requires no special treatment for backflow in slider bearings or special boundary conditions for heat transfer in the rupture zone of journal bearings.
A template for modeling thermo-hydrodynamic lubrication in journal bearings is presented. The model is validated using experimental and analytical data in the literature. Maximum deviation from measured temperatures is shown to be within 40 per cent. The model needs no special treatment of boundary conditions in the rupture zone and shows rapid and robust convergence which makes it quite suitable for use in design optimization models and in obtaining closed relations for critical parameters in the design of journal and slider bearings.
Empirically derived simulation models for temperature increase; leakage; and power loss are proposed and validated using the developed finite element model and experimental results from literature. Predictions of temperature increase, leakage, and power loss are better than those obtained for available relations in the literature. The derived simulation models include five important design variables namely the radial clearance, length to diameter ration, fluid viscosity, supply pressure and groove position. The derived model is used to minimize a multi-objective function using weight/scaling factors and Pareto optimal fronts. The latter method is recommended as preferable, and Pareto diagrams are presented for common bearing speeds. Including the groove location in the optimization model is shown to have a significant effect on the results. The lower bound of groove location appears to result in preferred power loss/side leakage values. Significant power loss savings may be realized with appropriate groove location.
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Souissi, Abderrazak. "Numerical simulation of one-dimensional and two-dimensional mass transport in groundwater, using Galerkin, Petrov-Galerkin and localized adjoint methods." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185695.
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Advection-diffusion transport equations are important in many branches of engineering and applied science. These equations are characterized by a nondissipative (hyperbolic) advective transport component and a dissipative (parabolic) diffusive component. When diffusion is the dominant process, most finite element numerical solution procedures perform well. However, when advection is the dominant transport process, most finite element numerical procedures exhibit some combination of excessive nonphysical oscillations and excessive numerical diffusion. Many numerical methods use Eulerian analysis to solve the advective diffusion equation. Some of them suffer from accuracy limitations, and others suffer from strict Courant number limitation. A Localized Adjoint Petrov-Galerkin Method is proposed to solve the multi-dimensional advection-diffusion equation. The method uses a weight function that is a numerical solution of adjoint state equations on a sequence of nested grids. Solutions corresponding to a given member of the sequence are ideally suited for parallel computation. One-dimensional numerical results are presented. The numerical results demonstrate that the method is accurate for low Peclet numbers. For large Peclet numbers numerical dispersion is introduced in the concentration profiles. Another method, the incomplete cubic Hermitian Galerkin, is presented to solve the transport equation for high Peclet number. One- and two-dimensional numerical results are presented. The numerical results demonstrate less oscillation and dispersion than obtained by linear Galerkin method.
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Ahmed, Naveed, and Gunar Matthies. "Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39044.
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We present the analysis for the higher order continuous Galerkin−Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin−Petrov and discontinuous Galerkin time discretization schemes will be given.
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Moosavi, Mohammad-Reza Khelil Abdelouahab. "Méthode combinée volumes finis et meshless local Petrov Galerkin appliquée au calcul de structures." S. l. : Nancy 1, 2008. http://www.scd.uhp-nancy.fr/docnum/SCD_T_2008_0080_MOOSAVI.pdf.
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Quezada, Celedon Julian Hermogenes. "Uma formulação de Petrov-Galerkin para problemas de dispersão pelo método dos elementos finitos." Universidade Federal do Rio de Janeiro, 1988. http://hdl.handle.net/11422/3876.
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Esta tese consiste na discussão de uma formulação de elementos finitos para a equação de difusão-convecção, utilizando um esquema de Petrov-Galerkin com funções de ponderação descontínuas. O esquema, conhecido como SUPG, introduz o conceito de "upwind" de maneira consistente, e pode ser facilmente aplicado a problemas transientes e/ou multidimensionais. Apresentam-se testes numéricos, uni e bidimensionais, para ilustrar as principais características do método de correção. As respostas obtidas são comparadas com resultados de outras formulações. Pode-se concluir, a partir dos casos analisados, que a correção adotada apresenta vantagens que justificam sua utilização em estudos práticos de dispersão.
This thesis consists in the discussion of a finite element formulation for the difusion-convection equation, using a Petrov-Galerkin scheme with discontinuous weighting functions. This scheme, known as SUPG, introduces the concept of a consistent upwind, that can be easily applied to transient and/or multidimensional problems. Numerical one and two-dirnensional tests are presented to illustrate the main characteristics of the correction method. Results are compared to the solutions obtained by other formulations. It can be concluded, based in the test results, that the proposed correction possesses several advantages which justify its utilization in practical dispersion studies.
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Bucur, Constantin 1967. "Finite element computations of transonic viscous flows with the streamline upwind Petrov-Galerkin (SUPG) formulation." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98947.
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Computations of transonic viscous flows are very challenging. The major difficulty comes from the discontinuity in the solution across a shock wave, causing undesired oscillations in the solution. In this work we focus on minimizing the oscillations by the use of a limiter to control the amount of diffusivity. This limiter provides the right amount of viscosity to capture a sharp shock and an accurate solution in high gradient regions. The limiter employs changes in pressure and entropy and has been implemented into the Streamline Upwind Finite Element Method. A mesh adaptation strategy has been employed to further enhance the accuracy of the solution. Results of simulations over RAE 2822 airfoil and ONERA M6 wing indicate significant improvements to the solution with this implementation.
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MOREUX, VINCENT. "Approximation par elements finis de type petrov-galerkin de systemes hyperboliques de lois de conservation." Toulouse 3, 1991. http://www.theses.fr/1991TOU30061.
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L'objet de ce travail est l'approximation numerique par elements finis des systemes hyperboliques d'equations non-lineaires, et en particulier des equations d'euler et la dynamique des gaz. Nous nous interessons ici plus particulierement a la classe des systemes hyperboliques k-diagonalisables telle que definie par p. A. Mazet, dont une grand part des systemes d'equations aux derivees partielles issues de la physique mathematique font partie. Cette motion, extension de la diagonalisabilite totale du cadre lineaire, exprime la propriete que possede un systeme de pouvoir s'ecrire comme moyenne d'equations scalaires lineaires. Les approximations par elements finis de ces systemes sont alors ramenees a celles d'equations de convection lineaires. Conformement a cette approche, on developpe ici la resolution de tels systemes, et en particulier du systeme des equations d'euler, par la methode de petrov-galerkin dans une version de type diffusion artificielle
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Ching, Hsu-Kuang. "Solution of Linear Elastostatic and Elastodynamic Plane Problems by the Meshless Local Petrov-Galerkin Method." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/28885.
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The meshless local Petrov-Galerkin (MLPG) method is used to numerically find an approximate solution of plane strain/stress linear elastostatic and elastodynamic problems. The MLPG method requires only a set of nodes both for the interpolation of the solution variables and the evaluation of various integrals appearing in the problem formulation. The monomial basis functions in the MLPG formulation have been enriched with those for the linear elastic fracture mechanics solutions near a crack tip. Also, the diffraction and the visibility criteria have been added to make the displacement field discontinuous across a crack. A computer code has been developed in Fortran and validated by comparing computed solutions of three static and one dynamic problem with their analytical solutions. The capabilities of the code have been extended to analyze contact problems in which a displacement component and the complementary traction component are prescribed at the same point of the boundary.
The code has been used to analyze stress and deformation fields near a crack tip and to find the stress intensity factors by using contour integrals, the equivalent domain integrals and the J-integral and from the intercepts with the ordinate of the plots, on a logarithmic scale, of the stress components versus the distance ahead of the crack tip. We have also computed time histories of the stress intensity factors at the tips of a central crack in a rectangular plate with plate edges parallel to the crack loaded in tension. These are found to compare favorably with those available in the literature. The code has been used to compute time histories of the stress intensity factors in a double edge-notched plate with the smooth edge between the notches loaded in compression. It is found that the deformation fields near the notch tip are mode-II dominant. The mode mixity parameter can be changed in an orthotropic plate by adjusting the ratio of the Young's moduli in the axial and the transverse direction.
The plane strain problem of compressing a linear elastic material confined in a rectangular cavity with rough horizontal walls and a smooth vertical wall has been studied with the developed code. Computed displacements and stresses are found to agree well with the analytical solution of the problem obtained by the Laplace transform technique.
The Appendix describes the analysis with the finite element code ABAQUS of the dependence of the energy release rate upon the crack length in a polymeric disk enclosed in a steel ring and having a star shaped hole at its center. A starter crack is assumed to exist in one of the leaflets of the hole. The disk is loaded either by a pressure acting on the surfaces of the hole and the crack or by a temperature rise. Computed values of the energy release rate obtained by modeling the disk material as Hookean are found to be about 30% higher than those obtained when the disk material is modeled as Mooney-Rivlin. The latter set of results accounts for both material and geometric nonlinearities.Ph. D.
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Hellwig, Friederike [Verfasser], Carsten [Gutachter] Carstensen, Rob [Gutachter] Stevenson, and Norbert [Gutachter] Heuer. "Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods / Friederike Hellwig ; Gutachter: Carsten Carstensen, Rob Stevenson, Norbert Heuer." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1189213397/34.
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Eyogo-Beyeme, Jean-Bernard. "Simulation numérique d'écoulements laminaires et turbulents à l'aide d'une formulation éléments finis de type Petrov-Galerkin." Lille 1, 2000. http://www.theses.fr/2000LIL10190.
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Brunken, Julia [Verfasser], and Mario [Akademischer Betreuer] Ohlberger. "Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations / Julia Brunken ; Betreuer: Mario Ohlberger." Münster : Universitäts- und Landesbibliothek Münster, 2021. http://d-nb.info/1235674886/34.
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Zhou, Yan. "Meshless Local Petrov-Galerkin method with Rankine source solution for two-dimensional two-phase flow modelling." Thesis, City University London, 2015. http://openaccess.city.ac.uk/14576/.
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A Lagrangian particle multiphase model based on the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R) is proposed to simulate 2D flows of two immiscible fluids. The model is applicable to fluids with a wide range of density ratio from 1.01 to 1000, capable of dealing with violent flow situations (e.g. breaking waves) and maintaining the sharp discontinuity of properties of the fluids at the interface. In order to extend the MLPG_R method to model multiphase flows, an innovative phase coupling is proposed using an equation for pressure at the interface particle through two stages. In the first stage, the formulation is based on ensuring the continuity of the pressure and the ratio of the pressure derivative in the normal direction of the interface to the fluid density across the interface. Gravity current, natural sloshing of two layered liquids and air-water violent sloshing are successfully simulated and compared with either experimental data or analytical solution demonstrating a second order convergent rate. The second stage involves the extension of the method to account for interface tension and large viscosity. This is achieved by adding additional terms in the original pressure formulation considering jumps for both the pressure and the ratio of pressure derivatives in either the normal or tangential direction to fluid density at the interface. The method ensures both velocity continuity even with highly viscous fluids and interface stress balance in the presence of interface tension. Simulation of square-droplet deformation illustrates sharp pressure drop at the interface and relieved spurious currents that are known to be associated with predictions by other existing models. The capillary wave case also demonstrates the necessity of maintaining the jump in the ratio of pressure gradient to fluid density and the bubble rising case further validates the model as compared with the benchmark numerical results. Apart from being the first application of the MLPG_R method to multiphase flows the proposed model also contains two highly effective and robust techniques whose applicability is not restricted to the MLPG_R method. One is based on use of the absolute density gradient for identifying the interface and isolated particles which is essential to ensure that interface conditions are applied at the correct locations in violent flows. The effectiveness of the technique has been examined by a number of particle configurations, including those with different levels of randomness of particle distribution. The other is about solving the discretised pressure equation, by splitting the one set equations into two sets corresponding to two phases and solving them separately but coupled by the interface particles. This technique efficiently gives reasonable solutions not only for the cases with low density ratio but also for the ones with very high density ratio.
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Ahuja, Kapil. "Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB." Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/34765.
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Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results.Master of Science
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D'Angelo, Stefano. "Adjoint-based error estimation for adaptive Petrov-Galerkin finite element methods: Application to the Euler equations for inviscid compressible flows." Doctoral thesis, Universite Libre de Bruxelles, 2015. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/228297.
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The current work concerns the study and the implementation of a modern algorithm for a posteriori error estimation in Computational Fluid Dynamics (CFD) simulations based on partial differential equations (PDEs). The estimate involves the use of duality argument and proper consistent discretisation of primal and dual problem.A key element is the construction of the adjoint form of the primal differential operators where the data term is a quantity of interest depending on the application. In engineering, this is typically a physical functional of the solution. So, by solving this adjoint problem, it is possible to obtain important information about local sensitivity of the error with respect to the current target quantity and thereby, we are able to perform an a posteriori error representation based on adjoint data. Through this, we provide local error indicators which can drive an adaptive meshing algorithm in order to optimally reduce the target error. Therefore, we first derive and solve the discrete primal problem in agreementwith the chosen numerical method. According to consistency and compatibility conditions, we can use the same discretisation for solving the adjoint problem, simply by swapping the position of the unknowns and the test functions in the linearised variational operator. Remembering that the corresponding adjoint problem always remains linear, the computational cost for obtaining these data is limited compared to the effort needed to solve the primal nonlinear problem.This procedure, fully developed for Discontinuous Galerkin (DG) and Finite Volume (FV) methods, is here for the first time applied in a fully consistent way for Petrov-Galerkin (PG) discretisations. Differently from the latter, the biggest issue for the PG method becomes the need to handle two different functional spaces in the discretisation, one of which is often not even continuous. Stabilized finite element schemes such as Streamline Upwind (SUPG), bubble stabilized (BUBBLE) Petrov-Galerkin and stabilized Residual Distribution (RD) have been selected for implementation and testing. Indeed, based on local advection information, these schemes are naturally more suitable for solving hyperbolic problems and therefore, interesting alternatives for fluid dynamics applications.A scalar linear advection equation is used as a model problem for convergence rate of both primal and adjoint solutions and target quantity. In addition, it is also applied in order to verify the accuracy of the adjoint-based a posteriori error estimate. Next, we apply the methods to a complete collection of numerical examples, starting from scalar Burgers’ problem till 2D compressible Euler equations. Through suited quantities of interest, we illustrate aspects of the adjoint mesh refinement by comparing its efficiency with respect to the standard a posteriori error estimation.Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Perella, Andrew James. "A class of Petrov-Galerkin finite element methods for the numerical solution of the stationary convection-diffusion equation." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5381/.
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A class of Petrov-Galerkin finite element methods is proposed for the numerical solution of the n dimensional stationary convection-diffusion equation. After an initial review of the literature we describe this class of methods and present both asymptotic and nonasymptotic error analyses. Links are made with the classical Galerkin finite element method and the cell vertex finite volume method. We then present numerical results obtained for a selection of these methods applied to some standard test problems. We also describe extensions of these methods which enable us to solve accurately for derivative values of the solution.
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Pereira, Dimitrius Caloghero. "Aproximação de Petrov-Galerkin para o escoamento de sangue em anastomoses sistêmico-pulmonares do tipo Blalock-Taussig modificada." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2001. http://hdl.handle.net/10183/3792.
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A anastomose sistêmico-pulmonar é um excelente procedimento paliativo para crianças e recém-nascidos portadores de cardiopatias congênitas cianóticas com diminuição da circulação pulmonar. Neste artigo, as aproximações “Streamline Upwind/Petrov-Galerkin – SUPG” foram utilizadas na simulação de escoamento de sangue em uma anastomose sistêmico pulmonar. A Anastomose estudada neste artigo é conhecido como Blalock-Taussig modificada no qual um enxerto de tubo sintético (prótese) é interposto entre a artéria subclávia esquerda e a artéria pulmonar com o objetivo de desviar parte do fluxo sistêmico ao pulmonar. A metodologia de elementos finitos utilizada, conhecida como método SUPG, supera as dificuldades enfrentadas pelo método de Galerkin clássico em altos números de Reynolds, que são compatibilizar os subespaços de velocidade e pressão – satisfazendo deste modo a condição denominada de Babuška-Brezzi e evitar oscilações espúrias devido à natureza assimétrica da aceleração advectiva de equação de momentum – adicionando termos malha-dependentes para a formulação de Galerkin clássica. Estes termos adicionais são construídos para aumentar a estabilidade da formulação de Galerkin original sem prejudicar sua consistência. Um modelo tridimensional parametrizado, utilizando o elemento lagrangeano trilinear, foi criado a partir de medições obtidas durante procedimento cirúrgico para avaliar os efeitos dos parametros geométricos envolvidos na cirurgia (diâmetro e ângulo do enxerto e a pulsatilidade do escoamento) Os resultados apresentam que o ângulo da anastomose proximal tem sensível influência na quantidade de fluxo desviada pelo enxerto e enorme influência na porcentagem de fluxo direcionado para cada um dos pulmões. Quanto ao diâmetro do enxerto conclui-se que este é o regulador principal da porcentagem de fluxo desviada. A partir das simulações realizadas determinou-se correlações para o fator de atrito e porcentagem de fluxo sangüíneo desviado pelo enxerto.
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Storn, Johannes [Verfasser], Carsten [Gutachter] Carstensen, Gerhard [Gutachter] Starke, and Dietmar [Gutachter] Gallistl. "Topics in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Analysis / Johannes Storn ; Gutachter: Carsten Carstensen, Gerhard Starke, Dietmar Gallistl." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1192302907/34.
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GUIMARÃES, Paulo Mohallem. "Análise da transferência de calor por convecção mista utilizando o método de elementos finitos com a técnica de Petrov-Galerkin." reponame:Repositório Institucional da UNIFEI, 2007. http://repositorio.unifei.edu.br/xmlui/handle/123456789/1713.
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Neste trabalho é apresentado um estudo numérico do escoamento laminar para convecção mista, empregando-se o Método de Elementos Finitos (MEF) utilizando elementos quadrilaterais com quatro nós, com as perturbações de Petrov−Galerkin nos termos convectivos, o método da penalidade nos termos de pressão e o esquema semi-implícito de Euler para avanço no tempo. Consideram-se escoamentos incompressíveis, bidimensionais e não-permanentes, sendo que os resultados são mostrados para o regime permanente em grande parte do trabalho. A formulação que governa os fenômenos físicos dos problemas baseia-se nas equações de conservação de massa, quantidade de movimento e energia. Foram realizadas comparações para a validação do código computacional e também um estudo do refinamento de malha. Quatro validações experimentais e numéricas são realizadas. Estudou se a independência da malha e verificação da convergência dos resultados para todos os casos. Finalmente, para os campos de velocidades, temperaturas e números de Nusselt local e médio, são apresentados resultados para canal com degrau na entrada, canal curvo, canal inclinado com fontes discretas de calor e cavidade com um ou dois cilindros internos rotativos. Verifica-se que a transferência de calor é fortemente influenciada por: i) no caso de canal com degrau e canal curvo, pelas células de recirculação, separação e recolamento; ii) para o canal com fontes discretas, pelo número de fontes, distância entre as fontes e a inclinação do canal; iii) para cavidade com cilindro interno rotativo pelo sentido e velocidade de rotação.
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Silva, Hugo Marcial Checo. "Elementos finitos em fluidos dominados pelo fenômeno de advecção: um método semi-Lagrangeano." Universidade do Estado do Rio de Janeiro, 2011. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8640.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorOs escoamentos altamente convectivos representam um desafio na simulação pelo método de elementos finitos. Com a solução de elementos finitos de Galerkin para escoamentos incompressíveis, a matriz associada ao termo convectivo é não simétrica, e portanto, a propiedade de aproximação ótima é perdida. Na prática as soluções apresentam oscilações espúrias. Muitos métodos foram desenvolvidos com o fim de resolver esse problema. Neste trabalho apresentamos um método semi- Lagrangeano, o qual é implicitamente um método do tipo upwind, que portanto resolve o problema anterior, e comparamos o desempenho do método na solução das equações de convecção-difusão e Navier-Stokes incompressível com o Streamline Upwind Petrov Galerkin (SUPG), um método estabilizador de reconhecido desempenho. No SUPG, as funções de forma e de teste são tomadas em espaços diferentes, criando um efeito tal que as oscilações espúrias são drasticamente atenuadas. O método semi-Lagrangeano é um método de fator de integração, no qual o fator é um operador de convecção que se desloca para um sistema de coordenadas móveis no fluido, mas restabelece o sistema de coordenadas Lagrangeanas depois de cada passo de tempo. Isto prevê estabilidade e a possibilidade de utilizar passos de tempo maiores.Existem muitos trabalhos na literatura analisando métodos estabilizadores, mas não assim com o método semi-Lagrangeano, o que representa a contribuição principal deste trabalho: reconhecer as virtudes e as fraquezas do método semi-Lagrangeano em escoamentos dominados pelo fenômeno de convecção.
Convection dominated flows represent a challenge for finite element method simulation. Many methods have been developed to address this problem. In this work we compare the performance of two methods in the solution of the convectiondiffusion and Navier-Stokes equations on environmental flow problems: the Streamline Upwind Petrov Galerkin (SUPG) and the semi-Lagrangian method. In Galerkin finite element methods for fluid flows, the matrix associated with the convective term is non-symmetric, and as a result, the best approximation property is lost. In practice, solutions are often corrupted by espurious oscillations. In this work, we present a semi- Lagrangian method, which is implicitly an upwind method, therefore solving the spurious oscillations problem, and a comparison between this semi-Lagrangian method and the Streamline Upwind Petrov Galerkin (SUPG), an stabilizing method of recognized performance. The SUPG method takes the interpolation and the weighting functions in different spaces, creating an effect so that the spurious oscillations are drastically attenuated. The semi-Lagrangean method is a integration factor method, in which the factor is an operator that shifts to a coordinate system that moves with the fluid, but it resets the Lagrangian coordinate system after each time step. This provides stability and the possibility to take bigger time steps. There are many works in the literature analyzing stabilized methods, but they do not analyze the semi-Lagrangian method, which represents the main contribution of this work: to recognize the strengths and weaknesses of the semi-Lagrangian method in convection dominated flows.
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Ghosh, Jayanto K. "Finite element simulation of non-Newtonian flow in the converging section of an extrusion die using a penalty function technique." Ohio : Ohio University, 1989. http://www.ohiolink.edu/etd/view.cgi?ohiou1172094913.
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Porfiri, Maurizio. "Analysis by Meshless Local Petrov-Galerkin Method of Material Discontinuities, Pull-in Instability in MEMS, Vibrations of Cracked Beams, and Finite Deformations of Rubberlike Materials." Diss., Virginia Tech, 2006. http://hdl.handle.net/10919/27420.
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The Meshless Local Petrov-Galerkin (MLPG) method has been employed to analyze the following linear and nonlinear solid mechanics problems: free and forced vibrations of a segmented bar and a cracked beam, pull-in instability of an electrostatically actuated microbeam, and plane strain deformations of incompressible hyperelastic materials. The Moving Least Squares (MLS) approximation is used to generate basis functions for the trial solution, and for the test functions. Local symmetric weak formulations are derived, and the displacement boundary conditions are enforced by the method of Lagrange multipliers. Three different techniques are employed to enforce continuity conditions at the material interfaces: Lagrange multipliers, jump functions, and MLS basis functions with discontinuous derivatives. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with the displacement iteration pull-in extraction algorithm. The analysis of large deformations of incompressible hyperelastic materials is performed by using a mixed pressure-displacement formulation. For every problem studied, computed results are found to compare well with those obtained either analytically or by the Finite Element Method (FEM). For the same accuracy, the MLPG method requires fewer nodes but more CPU time than the FEM.Ph. D.
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Elfverson, Daniel. "Multiscale Methods and Uncertainty Quantification." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262354.
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In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements. We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries. For uncertainty quantification problems we consider the estimation of p-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing p-quantiles and multilevel Monte Carlo methods for computing failure probability.
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Yin, Ping. "Sur une méthode numérique ondelettes / domaines fictifs lisses pour l'approximation de problèmes de Stefan." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10013/document.
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Notre travail est consacré à la définition, l'analyse et l'implémentation de nouveaux algorithmes numériques pour l'approximation de la solution de problèmes à 2 dimensions du type problème de Stefan. Dans ce type de problèmes une équation aux dérivée partielle parabolique posée sur un ouvert omega quelconque est couplée avec une autre équation qui contrôle la frontière gamma du domaine lui même. Les difficultés classiquement associés à ce type de problèmes sont: la formulation en particulier de l'équation pour le bord du domaine, l'approximation de la solution liées à la forme quelconque du domaine, les difficultés associées à l'implication des opérateurs de trace (approximation, conditionnement), les difficultés liées aux de régularité fonds du domaine.De plus, de nombreuse situations d'intérêt physique par exemple demandent des approximations de haut degré. Notre travail s'appuie sur une formulation de type espaces de niveaux (level set) pour l'équation du domaine, et une formulation de type domaine fictif (Omega) pour l'équation initiale.Le contrôle des conditions aux limites est effectué à partir de multiplicateurs de Lagrange agissant sur une frontière (Gamma) dite de contrôle différente de frontière(gamma) du domaine (omega). L'approximation est faite à partir d'un schéma aux différences finies pour les dérivées temporelle et une discrétisation à l'aide d'ondelettes bi-dimensionelles pour l'équation initiale et une dimensionnelle pour les multiplicateurs de Lagrange. Des opérateurs de prolongement de omega à Omega sont également construits à partir d'analyse multiéchelle sur l'intervalle. Nous obtenons aussi: une formulation pour laquelle existence de la solution est démontrées, un algorithme convergent pour laquelle une estimation globale d'erreur (sur Omega) est établie, une estimation intérieure prouvant sur l'erreur à un domaine omega, overline omega subset Xi, des estimations sur les conditionnement associés a l'opérateur de trace, des algorithmes de prolongement régulier. Différentes expériences numériques en 1D ou 2D sont effectuées. Le manuscrit est organisé comme suit: Le premier chapitre rappelle la construction des analyses multirésolutions, les propriétés importantes des ondelettes et des algorithmes numériques liées à l'application d'opérateurs aux dérivées partielles. Le second chapitre donne un aperçu des méthodes de domaine fictif classiques, approchées par la méthode de Galerkin ou de Petrov-Galerkin. Nous y découvrons les limites de ces méthodes ce qui donne la direction de notre travail. Le chapitre trois présente notre nouvelle méthode de domaine fictif que l'on appelle méthode de domaine fictif lisse.L'approximation est grâce à une méthode d'ondelettes de type Petrov-Galerkin. Cette section contient l'analyse théorique et décrit la mise en œuvre numérique. Différents avantages de cette méthode sont démontrés. Le chapitre quatre introduit une technique de prolongement régulier. Nous l'appliquons à des problèmes elliptiques en 1D ou 2D.\par Le cinquième chapitre décrit quelques simulations numériques de problème de Stefan. Nous testons l'efficacité de notre méthode sur différents exemples dont le problème de Stefan à 2 phases avec conditions aux limites de Gibbs-ThomsonOur work is devoted to the definition, analysis and implementation of a new algorithms for numerical approximation of the solution of 2 dimensional Stefan problem. In this type of problem a parabolic partial differential equation defined on an openset Omega is coupled with another equation which controls the boundary gamma of the domain itself. The difficulties traditionally associated with this type of problems are: the particular formulation of equation on the boundary of domain, the approximation of the solution defined on general domain, the difficulties associated with the involvement of trace operation (approximation, conditioning), the difficulties associated with the regularity of domain. Addition, many situations of physical interest, for example,require approximations of high degree. Our work is based on aformulation of type level set for the equation on the domain, and aformulation of type fictitious domain (Omega) for the initialequation. The control of boundary conditions is carried out throughLagrange multipliers on boundary (Gamma), called control boundary, which is different with boundary (gamma) of the domain (omega). The approximation is done by a finite difference scheme for time derivative and the discretization by bi-dimensional wave letfor the initial equation and one-dimensional wave let for the Lagrange multipliers. The extension operators from omega to Omega are also constructed from multiresolution analysis on theinterval. We also obtain: a formulation for which the existence of solution is demonstrated, a convergent algorithm for which a global estimate error (on Omega) is established, interior error estimate on domain omega, overline omega subset estimates on the conditioning related to the trace operator, algorithms of smooth extension. Different numerical experiments in 1D or 2D are implemented. The work is organized as follows:The first chapter recalls theconstruction of multiresolution analysis, important properties of wavelet and numerical algorithms. The second chapter gives an outline of classical fictitious domain method, using Galerkin or Petrov-Galerkin method. We also describe the limitation of this method and point out the direction of our work.\par The third chapter presents a smooth fictitious domain method. It is coupled with Petrov-Galerkin wavelet method for elliptic equations. This section contains the theoretical analysis and numerical implementation to embody the advantages of this new method. The fourth chapter introduces a smooth extension technique. We apply it to elliptic problem with smooth fictitious domain method in 1D and 2D. The fifth chapter is the numerical simulation of the Stefan problem. The property of B-spline render us to exactly calculate the curvature on the moving boundary. We use two examples to test the efficiency of our new method. Then it is used to resolve the two-phase Stefan problem with Gibbs-Thomson boundary condition as an experimental case
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GREFF, Isabelle. "Schemas boite : Etude theorique et numerique." Phd thesis, Université de Metz, 2003. http://tel.archives-ouvertes.fr/tel-00005922.
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Dans cette these, nous etudions les schemas boite. Ils ont ete introduits par H.B. Keller en 1971. Dans un premier temps, on s'est interesse a des problemes elliptiques de type Poisson. Plusieurs schemas boite pour des domaines de $\mathbb(R)^2$ mailles par des triangles ou des rectangles ont ete introduits. Dans ce cas, la discretisation s'effectue sur la forme mixte du probleme en prenant la moyenne des deux equations (conservation et flux) sur les cellules du maillage. La methode peut etre qualifiee de ``methode volumes finis mixte de type Petrov-Galerkin ``. Une des difficultes du design de cette famille de schemas reside dans le choix des differents espaces de fonctions (approximation et test) qui doivent satisfaire des conditions de compatibilite de type Babuska-Brezzi. En revanche, cette methode de discretisation ne necessite qu'un seul maillage (le maillage du domaine). De plus, on montre dans la plupart des cas que le schema obtenu est equivalent a un probleme découplé : la résolution d'un probleme variationnel pour l'inconnue principale et une formule locale pour le gradient (le flux). Cette formulation facilite le calcul des inconnues discretes. Des resultats de stabilite et les calculs d'erreurs reposant sur la theorie des elements finis ont ete etablis. Une etude numérique valide ces resultats pour quelques cas tests. Dans le cadre du Groupement de Recherche MoMaS pour le stockage des dechets nucleaires dans la Meuse, j'ai ensuite etudie des problemes de convection-diffusion instationnaires. Un schéma boite permettant d'approcher ces equations dans le cas monodimensionnel a ete introduit. Des coefficients de decentrement propres a chaque maille permettent de controler le schema (precision, stabilite). Afin de generaliser rapidement ce schema au cas bidimensionnel, je me suis concentree sur une extension du schema boite monodimensionnel par la methode ADI (Alternating Direction Implicit).
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Wells, David Reese. "Stabilization of POD-ROMs." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/52960.
Full textAbstract:
This thesis describes several approaches for stabilizing POD-ROMs
(that is, reduced order models based on basis functions derived from the proper
orthogonal decomposition) for both the CDR (convection-diffusion-reaction)
equation and the NSEs (Navier-Stokes equations). Stabilization is necessary
because standard POD-ROMs of convection-dominated problems usually display
numerical instabilities.
The first stabilized ROM investigated is a streamline-upwind
Petrov-Galerkin ROM (SUPG-ROM). I prove error estimates for the SUPG-ROM and
derive optimal scalings for the stabilization parameter. I test the SUPG-ROM
with the optimal parameter in the numerical simulation of a convection-dominated
CDR problem. The SUPG-ROM yields more accurate results than the standard
Galerkin ROM (G-ROM) by eliminating the inherent numerical artifacts (noise) in
the data and dampening spurious oscillations.
I next propose two regularized ROMs (Reg-ROMs) based on ideas from large
eddy simulation and turbulence theory: the Leray ROM (L-ROM) and the
evolve-then-filter ROM (EF-ROM). Both Reg-ROMs use explicit POD spatial
filtering to regularize (smooth) some of the terms in the standard G-ROM. I
propose two different POD spatial filters: one based on the POD projection and a
novel POD differential filter. These two new Reg-ROMs and the two spatial
filters are investigated in the numerical simulation of the three-dimensional
flow past a circular cylinder problem at Re = 100. The numerical results
show that EF-ROM-DF is the most accurate Reg-ROM and filter combination and the
differential filter generally yields better results than the projection filter.
The Reg-ROMs perform significantly better than the standard G-ROM and decrease
the CPU time (compared against the direct numerical simulation) by orders of
magnitude (from about four days to four minutes).Ph. D.
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Mollet, Christian [Verfasser], Ulrich [Gutachter] Trottenberg, Guido [Gutachter] Sweers, and Olaf [Gutachter] Steinbach. "Parabolic PDEs in Space-Time Formulations: Stability for Petrov-Galerkin Discretizations with B-Splines and Existence of Moments for Problems with Random Coefficients / Christian Mollet. Gutachter: Ulrich Trottenberg ; Guido Sweers ; Olaf Steinbach." Köln : Universitäts- und Stadtbibliothek Köln, 2016. http://d-nb.info/1110071027/34.
Full text
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ONO, SHIZUCA. "Modelos aproximados para o calculo do transporte de particulas neutras em dutos." reponame:Repositório Institucional do IPEN, 2000. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10788.
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Made available in DSpace on 2014-10-09T12:44:01Z (GMT). No. of bitstreams: 0Made available in DSpace on 2014-10-09T14:07:20Z (GMT). No. of bitstreams: 1 06913.pdf: 2715369 bytes, checksum: 9d927e16226a25d1d362ba0ebc83502c (MD5)
Tese (Doutoramento)
IPEN/T
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Ghadi, Fatth-Allah. "Résolution par la méthode des éléments finis des équations de Navier-Stokes en formulation (v-w)." Saint-Etienne, 1994. http://www.theses.fr/1994STET4010.
Full textAbstract:
Dans ce travail, nous proposons une méthode mixte en fonction de courant-tourbillon pour résoudre le problème de Stokes dans des domaines bornes réguliers de r. Nous établissons par la suite des estimations d'erreur dans le cadre des formulations mixtes classiques. Du point de vue numérique, nous mettons en oeuvre une méthode basée sur l'approximation d'une base harmonique pour résoudre le problème de Stokes. Par ailleurs nous étendons cette méthode au cas du problème de Navier-Stokes et afin de combattre la convection dominante nous faisons appel à la technique de Petrov-Galerkin
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Bezier, Florence. "Problèmes de transport-diffusion par éléments finis." Compiègne, 1990. http://www.theses.fr/1990COMPD255.
Full textAbstract:
Cette étude décrit un ensemble de méthodes numériques applicables aux problèmes de transport-diffusion. Ceci est développé dans un contexte éléments finis. Néanmoins une synthèse des recherches effectuées dans ce domaine est faite et un grand nombre de références bibliographiques est donné. Un rappel des équations de mécanique des fluides est faite pour des fluides incompressible, compressible, turbulent, des écoulements à surface libre et pour le charriage et la suspension des sédiments. Puis nous décrivons rapidement les formulations variationnelles et la discrétisation par éléments finis de chacun de ces problèmes. Avant de présenter des méthodes plus sophistiquées, nous rappelons les méthodes de Newton, Quasi-Newton et les méthodes de gradient conjugué généralisé. Puis nous abordons l'étude de l'équation modèle de transport-diffusion en non-stationnaire. Une étude de la stabilité et de la connaissance des schémas d'Euler nous conduisant aux méthodes de Taylor-Galerkin. Pour chaque schéma numérique, nous calculons l'équation équivalente, le facteur d'amplification et la vitesse de phase. De cette étude nous retenons 3 algorithmes. Ces algorithmes utilisent la méthode des pas fractionnaires. Puis une approche stationnaire est abordée. Nous rappelons les méthodes de Petrov-Galerkin et proposons une nouvelle méthode permettant d'obtenir une solution exacte aux nœuds et ceci sans condition sur le maillage. Enfin un certain nombre de résultats significatifs est proposé.
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Seymen, Zahire. "Solving Optimal Control Time-dependent Diffusion-convection-reaction Equations By Space Time Discretizations." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615399/index.pdf.
Full textAbstract:
Optimal control problems (OCPs) governed by convection dominated diffusion-convection-reaction
equations arise in many science and engineering applications such as shape optimization of the technological
devices, identification of parameters in environmental processes and flow control problems.
A characteristic feature of convection dominated optimization problems is the presence of sharp layers.
In this case, the Galerkin finite element method performs poorly and leads to oscillatory solutions.
Hence, these problems require stabilization techniques to resolve boundary and interior layers accurately.
The Streamline Upwind Petrov-Galerkin (SUPG) method is one of the most popular stabilization
technique for solving convection dominated OCPs.
The focus of this thesis is the application and analysis of the SUPG method for distributed and
boundary OCPs governed by evolutionary diffusion-convection-reaction equations. There are two approaches
for solving these problems: optimize-then-discretize and discretize-then-optimize. For the
optimize-then-discretize method, the time-dependent OCPs is transformed to a biharmonic equation,
where space and time are treated equally. The resulting optimality system is solved by the finite
element package COMSOL. For the discretize-then-optimize approach, we have used the so called allv
at-once method, where the fully discrete optimality system is solved as a saddle point problem at once
for all time steps. A priori error bounds are derived for the state, adjoint, and controls by applying
linear finite element discretization with SUPG method in space and using backward Euler, Crank-
Nicolson and semi-implicit methods in time. The stabilization parameter is chosen for the convection
dominated problem so that the error bounds are balanced to obtain L2 error estimates. Numerical examples
with and without control constraints for distributed and boundary control problems confirm the
effectiveness of both approaches and confirm a priori error estimates for the discretize-then-optimize
approach.
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Ghilani, Mustapha. "Simulation numérique de flammes planes stationnaires avec chimie complexe." Paris 11, 1987. http://www.theses.fr/1987PA112325.
Full textAbstract:
L'objectif de cette thèse est la résolution numérique d'un système d'équations différentielles non-linéaire décrivant une flamme plane stationnaire, avec chimie complexe et modèles de transport et de diffusion réalistes, par la méthode des éléments finis décentrés de Petrov-Galerkin. Du point de vue numérique nous montrons que l'utilisation de la méthode de Petrov-Galerkin supprime les instabilités spatiales qui apparaissent lors de l'utilisation d'un schéma centré, ce qui augmente la robustesse du schéma sans détériorer sa précision. Du point de vue mathématique nous présentons un nouveau résultat concernant l'analyse numérique des méthodes implicites utilisées pour le calcul des flammes stationnaires. Trois études ont été réalisées par cette méthode sur la flamme d'oxydation d'hydrogène dans l'air: la première sur une flamme stœchiométrique, la deuxième sur la variation de la vitesse de propagation de la flamme avec la richesse du mélange, et la troisième sur un phénomène d'extinction purement cinétique.
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Nadukandi, Prashanth. "Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/109155.
Full textAbstract:
We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction
(CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a
consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was
ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory
numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to
convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution
Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent
approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of
he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi:
10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is
used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good
shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the
Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to
ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the
problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi
dimensional extension of the HRPG method using multi-linear block finite elements is also presented.
Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz
equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method
(FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation
method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover
he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045-
7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the
analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi:
10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion
accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an
expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin
ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the
error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small.Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion
48
Wakrim, Mohamed. "Analyse numérique des équations de Navier-Stokes incompressibles et simulations dans des domaines axisymétriques." Saint-Etienne, 1993. http://www.theses.fr/1993STET4015.
Full textAbstract:
Dans cette thèse, on a développé une méthode numérique pour la simulation des écoulements de fluides à nombre de Reynolds élevé, utilisant deux types d'éléments finis. On a établi la convergence de l'algorithme d'Uzawa en formulation de Petrov-Galerkin et on a étudié l'élément fini de Crouzeix-Raviart en formulation de Petrov-Galerkin. Pour finir, on a construit un préconditionneur du CGS pour une formulation couplée
49
Slemp, Wesley Campbell Hop. "Integrated Sinc Method for Composite and Hybrid Structures." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/77111.
Full textAbstract:
Composite materials and hybrid materials such as fiber-metal laminates, and functionally graded materials are increasingly common in application in aerospace structures. However, adhesive bonding of dissimilar materials makes these materials susceptible to delamination. The use of integrated Sinc methods for predicting interlaminar failure in laminated composites and hybrid material systems was examined. Because the Sinc methods first approximate the highest-order derivative in the governing equation, the in-plane derivatives of in-plane strain needed to obtain interlaminar stresses by integration of the equilibrium equations of 3D elasticity are known without post-processing. Interlaminar stresses obtained with the Sinc method based on Interpolation of Highest derivative were compared for the first-order and third-order shear deformable theories, the refined zigzag beam theory and the higher-order shear and normal deformable beam theory. The results indicate that the interlaminar stresses by the zigzag theory compare well with those obtained by a 3D finite element analysis, while the traditional equivalent single layer theories perform well for some laminates.
The philosophy of the Sinc method based on Interpolation of Highest Derivative was extended to create a novel weak form based approach called the Integrated Local Petrov-Galerkin Sinc Method. The Integrated Local Petrov-Galerkin Sinc Method is easily utilized for boundary-value problem on non-rectangular domains as demonstrated for analysis of elastic and elastic-plastic plane-stress panels with elliptical notches. The numerical results showed excellent accuracy compared to similar results obtained with the finite element method.
The Integrated Local Petrov-Galerkin Sinc Method was used to analyze interlaminar debonding of composite and fiber-metal laminated beams. A double-cantilever beam and a fixed-ratio mixed mode beam were analyzed using the Integrated Local Petrov-Galerkin Sinc Method and the results were shown to correlate well with those by the finite element method. An adaptive Sinc point distribution technique was implemented for the delamination analysis which significantly improved the methods accuracy for the present problem. Delamination of a GLARE, plane-strain specimen was also analyzed using the Integrated Local Petrov-Galerkin Sinc Method. The results correlate well with 2D, plane-strain analysis by the finite element method, including interlaminar stresses obtained by through-the-thickness integration of the equilibrium equations of 3D elasticity.Ph. D.
50
Bertic, Yves. "Modélisation et caractérisation de capteurs mécano-optiques en optique intégrée à base d'INP." Saint-Etienne, 1997. http://www.theses.fr/1997STET4013.
Full textAbstract:
Ce mémoire présente la modélisation et la caractérisation de capteurs de pression et d'accélération en optique intégrée à base de semi-conducteurs III-V (filière INGAALAS/INP). Après une revue générale des capteurs opto-mécaniques et des différentes techniques de modulation utilisées en optique intégrée, les dispositifs retenus sont présentés. Un logiciel de résolution de l'équation d'onde vectorielle basé sur la méthode de Galerkin est développé afin de concevoir des guides optiques monomodes compatibles avec le micro-usinage des dispositifs. La modélisation du comportement mécanique des structures étudiées (plaque mono-encastrée et plaque encastrée sur ses quatre cotés) est effectuée sur la base des hypothèses de la résistance des matériaux. L'effet photoélastique est introduit et une expression théorique de la variation d'indice effectif sous l'action d'une déformation est donnée. Les paramètres opto-mécaniques des matériaux semi-conducteurs III-V utilisés (indices de réfraction et coefficients photoélastiques notamment) sont également calculés à l'aide du modèle d'Adachi basé sur les transitions interbandes électron-trou. La sensibilité théorique des capteurs de pression et d'accélération est alors évaluée sur la base des outils de modélisation précédemment développés. Enfin, les étapes clefs de la fabrication des dispositifs par micro-usinage de volume en face arrière sont présentées et des capteurs de pression sont caractérisés en configuration guide droit sur membrane (modulation de polarisation) puis en configuration interféromètre de Mach-Zehnder sur membrane (modulation de phase). Des différences de pression de 1 Mbar ont pu être mesurées démontrant la faisabilité d'un tel dispositif