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1
Yildirim, B. Gazi. "A global preconditioning method for the Euler equations." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-07152003-164237.
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Voonna, Kiran. "Development of discontinuous galerkin method for 1-D inviscid burgers equation." ScholarWorks@UNO, 2003. http://louisdl.louislibraries.org/u?/NOD,75.
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Thesis (M.S.)--University of New Orleans, 2003.<br>Title from electronic submission form. "A thesis ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering"--Thesis t.p. Vita. Includes bibliographical references.
3
Brock, Jerry S. "A consistent direct-iterative inverse design method for the Euler equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40033.
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A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic
test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods.<br>Ph. D.
4
Ramos, Manoel Wallace Alves. "Métodos de Euler e Runge-Kutta: uma análise utilizando o Geogebra." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9381.
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Previous issue date: 2017-06-19<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Is evident the importance of ordinary differential equations in modeling problems
in several areas of science. Coupled with this, is increasing the use of numerical
methods to solve such equations. Computers have become an extremely useful tool
in the study of differential equations, since through them it is possible to execute
algorithms that construct numerical approximations for solutions of these equati-
ons. This work introduces the study of numerical methods for ordinary differential
equations presenting the numerical Eulerºs method, improved Eulerºs method and
the class of Runge-Kuttaºs methods. In addition, in order to collaborate with the
teaching and learning of such methods, we propose and show the construction of
an applet created from the use of Geogebm software tools. The applet provides
approximate numerical solutions to an initial value problem, as well as displays the
graphs of the solutions that are obtained from the numerical Eulerºs method, im-
proved Eulerºs method, and fourth-order Runge-Kuttaºs method.<br>É evidente a importancia das equações diferenciais ordinarias na modelagem de
problemas em diversas áreas da ciência, bem como o uso de métodos numéricos para
resolver tais equações. Os computadores são uma ferramenta extremamente útil no
estudo de equações diferenciais, uma vez que através deles é possível executar algo-
ritmos que constroem aproximações numéricas para soluções destas equações. Este
trabalho é uma introdução ao estudo de métodos numéricos para equações diferen-
ciais ordinarias. Apresentamos os métodos numéricos de Euler, Euler melhorado e a
classe de métodos de Runge-Kutta. Além disso, com o propósito de colaborar com o
ensino e aprendizagem de tais métodos, propomos e mostramos a construção de um
applet criado a partir do uso de ferramentas do software Geogebra. O applet fornece
soluções numéricas aproximadas para um problema de valor inicial, bem como eXibe
os graficos das soluções que são obtidas a partir dos métodos numéricos de Euler,
Euler melhorado e Runge-Kutta de quarta ordem.
5
Tam, Laying. "The general Euler-Borel summability method /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683756124139.
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Helin, Mikael. "Inverse Parameter Estimation using Hamilton-Jacobi Equations." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123092.
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Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare given<br>I detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.
7
Artale, Valeria. "Level-Set Ghost Fluid Methods for Free Boundary Problems in Incompressible Euler and Navier-Stokes Equations." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1106.
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The present work is devoted to the study of free boundary problems for Euler and Navier-Stokes equations in primitive variables. The goal of the present work is to elaborate a methodology for numerical modeling of all kinds of incompressible viscous fluids, having in mind possible application to deep water, lava flow simulation and crust formation.
Our approach could be essentially divided in three fundamental components: finite difference for spatial approximation, second order accurate method for temporal discretization and level set methods for boundary representation.
The domain is discretized by a regular Cartesian grid. The boundary is described by level set methods. In this context the boundary is seen as a zero level set of a specific function. Navier-Stokes equations is solved starting from Semi-Lagrangian methods, achieving second order accuracy in time and space. Resolution of Navier-Stokes equations allows a Poisson problem for pressure as an intermediate step. This is solved by multigrid methods. The velocity and the pressure are computed by solving a single implicit system solved iteratively.
8
Kurz, Dominik [Verfasser]. "Numerische Simulation industrieller Rostfeuerungen nach der Euler-Euler Methode / Dominik Kurz." Aachen : Shaker, 2014. http://d-nb.info/1066196338/34.
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Rückert, Frank. "Simulation von Festbettreaktoren zur technischen Verbrennung mit der Euler-Euler-Methode /." Düsseldorf : VDI-Verl, 2007. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015625261&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Rückert, Frank. "Simulation von Festbettreaktoren zur technischen Verbrennung mit der Euler/Euler-Methode." [S.l. : s.n.], 2005. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-29685.
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Choi, Sang Keun. "A Cartesian finite-volume method for the Euler equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/76511.
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A numerical procedure has been developed for the computation of inviscid flows over arbitrary, complex two-dimensional geometries. The Euler equations are solved using a finite-volume method with a non-body-fitted Cartesian grid. A new numerical formulation for complicated body geometries is developed in conjunction with implicit flux-splitting schemes. A variety of numerical computations have been performed to validate the numerical methodologies developed. Computations for supersonic flow over a flat plate with an impinging shock wave are used to verify the numerical algorithm, without geometric considerations. The supersonic flow over a blunt body is utilized to show the accuracy of the non-body-fitted Cartesian grid, along with the shock resolution of flux-vector splitting scheme. Geometric complexities are illustrated with the flow through a two-dimensional supersonic inlet with and without an open bleed door. The ability of the method to deal with subsonic and transonic flows is illustrated by computations over a non-lifting NACA 0012 airfoil. The method is shown to be accurate, efficient and robust and should prove to be particularly useful in a preliminary design mode, where flows past a wide variety of complex geometries can be computed without complicated grid generation procedures.<br>Ph. D.
12
Zimmermann, Susanne A. "Properties of the method of transport for the Euler equations /." [S.l.] : [s.n.], 2001. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13957.
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Nazarov, Murtazo. "An adaptive finite element method for the compressible Euler Equations /." Licentiate thesis, Stockholm : Skolan för datavetenskap och kommunikation, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10582.
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Paisley, M. F. "Finite volume methods for the steady Euler equations." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375309.
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Megbil, Ihab. "Algebraiska och geometriska lösningar av kubiska ekvationer." Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-27057.
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Syftet med det här arbetet är att lösa kubiska ekvationer utifrån både algebraiska och geometriska perspektiv. Läsaren kommer att möta olika metoder att finna rötter av kubiska ekvationer med fokus på Cardanos metod. Kapitel 3 introducerar Khayyams metod för att hitta en positiv reell rot med hjälp av geometrisk algebra. Kapitel 4 presenterar Cardanos metod för att hitta en positiv reell rot med geometrisk och algebraisk metod. Kapitel 5 visar bisektionsmetoden och Newton-Raphsons metod för att hitta en reell rot med numeriska beräkningar. För att underlätta metoder (för moderna ögon) använde jag mig av spel, tabeller och moderna matematikprogram. Förståelsen av dessa metoder med faktorsatsen visas i kapitel 6 hur vi kan hitta alla reella rötter när vi har en rot. Dessutom innehåller kapitlet Cardanos formel för tre rötter av den allmänna kubiska ekvationen. Kapitel 7 presenterar Eulers metod för att lösa den allmänna bikvadratiska ekvationen med hjälp av Cardanos metod. Dessutom beskrivs Descartes metod för att lösa bikvadratiska ekvationer med användningen av geometriskalgebra. Läsaren får även en inblick i kvintiska ekvationer.
16
Guillermo-Monedero, Daniel. "A Comparison of Euler Finite Volume and Supersonic Vortex Lattice Methods used during the Conceptual Design Phase of Supersonic Delta Wings." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1576713976622162.
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Wysocki, Stefan. "Joint Euler-Lagrange method for moving surfaces in large-eddy simulation." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/10214.
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Continuous growth of computing power strongly encourages engineers to rely more on computational fluid dynamics for the design and testing of new technological solutions. The fast development of these new tools goes along with the increasing availability of high-performance computers, which are necessary to simulate realistic industrial applications. The presented immersed boundary (IB) method is applicable to simple and complex geometries with static and moving boundaries, where fluids interact with the solid structures. The formulation of the method is based on the Eulerian and Lagrangian principles and its key characteristics are its simple formulation and computational efficiency. Furthermore the nature of the method allows the simulations of flows in complex geometries without having to generate complex meshes. The spatial discretization is based on a fixed Cartesian mesh for the Eulerian variables and boundary movements are tracked with Lagrangian particles. Large- Eddy simulations of flows in simple and complex geometries demonstrate the performance of the applied immersed boundary method. Simple cases include the simulation of an isothermal pipe flow and the flow around a sphere. In the first instance, the fluid flows around a static sphere. In the second case the sphere moves relative to the grid for identical flow conditions. Simulations of complex geometries include the investigation of an isothermal and reactive opposed jet flow with perforated and fractal grids. The simulations require cell sizes near the resolution of direct numerical simulations. The injection phase of a piston-cylinder arrangement, assuming constant pressure, is also investigated with the proposed IB method. Good statistical results for first and second moments are achieved for all investigated cases, although the applied grids have to be fine enough to accurately resolve the wall shear stresses. In addition, the concept of using Lagrangian particles has been applied to immiscible flows. Particles are used to improve the accuracy of scalar transport and initial results of simple, two-dimensional test cases are presented.
18
Hartmann, Ralf. "Adaptive finite element methods for the compressible Euler equations." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964933071.
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Edwards, M. G. "Moving element methods with emphasis on the Euler equations." Thesis, University of Reading, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378193.
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Türk, Serhat, and Kristoffer Müller. "Kinetic Art Table : Polar sand plotter." Thesis, KTH, Mekatronik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-296307.
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CNC machines are used with plenty of different implementations, one of which is in this project where a polar CNC machine was used to draw mesmerizing patterns on a table with fine sand. This construction read G-code and converted it to polar coordinates. The capabilities of what the plotter could draw were tested, everything from ODE plots to custom-made patterns and drawings with the help of Sandify. Although the patterns were drawn properly with small errors the ODE was too difficult to draw because it required a smaller magnetic ball and an even more precise system than what was used. This machine also generated noise at roughly 33 dB when it was in use.<br>CNC-maskiner används med massor av olika implementationer, en av dem är i det här projektet där en polar CNC maskin användes för att rita fascinerande mönster på ett bord fylld med fin sand. Denna konstruktion läste in G-kod och konverterade det till polära koordinater. Förmågan av vad maskinen kunde rita testades, allt från ODE grafer till specialtillverkade mönster och ritningar med hjälp av Sandify. Aven om de olika mönstren ritades ordentligt men med mindre små fel var ODE för svårt att rita på grund av att det krävde en mindre magnetisk kula och ännu mer noggrannhet jämfört med detta system. Denna maskin alstrade också ljud på cirka 33 dB under användning.
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Pueyo, Alberto. "An efficient Newton-Krylov method for the Euler and Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq35288.pdf.
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Tantardini, F. "QUASI-OPTIMALITY IN THE BACKWARD EULER-GALERKIN METHOD FOR LINEAR PARABOLIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/229462.
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We analyse the backward Euler-Galerkin method for linear parabolic problems, looking for quasi-optimality results in the sense of Céa's Lemma. We cast the problem into the framework given by the inf-sup theory, and we analyse the spatial discretization, the discretization in time and the topic of varying the spatial discretization separately.
Concerning the spatial discretization, we prove the the H1-stability of the L2-projection is also a necessary condition for quasi-optimality, both in the H1(H-1)∩L2(H1)-norm and in the L2(H1)-norm.
Concerning the discretization in time, we prove that the error in a norm that mimics the H1(H-1)∩L2(H1)-norm is equivalent to the sum of the best errors with piecewise constants for the exact solution and its time derivative, if the partition is locally quasi-uniform.
Turning to the topic of varying the spatial dicretization, we provide a bound for the error that includes the best error and an additional term, which vanishes if there are not modifications of the spatial dicretization and which is consistent with the example of non convergence in Dupont '82. We combine these elements in an analysis of the backward Euler-Galerkin method and derive error estimates in case the spatial discretization is based on finite elements.
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Bulgok, Murat. "A Quadtree-based Adaptively-refined Cartesian-grid Algorithm For Solution Of The Euler Equations." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606687/index.pdf.
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A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based
adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to advance the solution in time. A number of internal and
external flow problems are solved in order to demonstrate the efficiency and accuracy of the method.
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C, Praveen. "Development and Application of Kinetic Meshless Methods for Euler Equations." Thesis, Indian Institute of Science, 2004. https://etd.iisc.ac.in/handle/2005/154.
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Meshless methods are a relatively new class of schemes for the numerical solution of partial differential equations. Their special characteristic is that they do not require a mesh but only need a distribution of points in the computational domain. The approximation at any point of spatial derivatives appearing in the partial differential equations is performed using a local cloud of points called the "connectivity" (or stencil). A point distribution can be more easily generated than a grid since we have less constraints to satisfy.
The present work uses two meshless methods; an existing scheme called Least Squares Kinetic Upwind Method (LSKUM) and a new scheme called Kinetic Meshless Method (KMM). LSKUM is a "kinetic" scheme which uses a "least squares" approximation} for discretizing the derivatives occurring in the partial differential equations. The first part of the thesis is concerned with some theoretical properties and application of LSKUM to 3-D point distributions. Using previously established results we show that first order LSKUM in 1-D is positivity preserving under a CFL-like condition. The 3-D LSKUM is applied to point distributions obtained from FAME mesh. FAME, which stands for Feature Associated Mesh Embedding, is a composite overlapping grid system developed at QinetiQ (formerly DERA), UK, for store separation problems.
The FAME mesh has a cell-based data structure and this is first converted to a node-based data structure which leads to a point distribution. For each point in this distribution we find a set of nearby nodes which forms the connectivity. The connectivity at each point (which is also the "full stencil" for that point) is split along each of the three coordinate directions so that we need six split (or half or one-sided) stencils at each point. The split stencils are used in LSKUM to calculate the split-flux derivatives arising in kinetic schemes which gives the upwind character to LSKUM. The "quality" of each of these stencils affects the accuracy and stability of the numerical scheme. In this work we focus on developing some numerical criteria to quantify the quality of a stencil for meshless methods like LSKUM.
The first test is based on singular value decomposition of the over-determined problem and the singular values are used to measure the ill-conditioning (generally caused by a flat stencil). If any of the split stencils are found to be ill-conditioned then we use the full stencil for calculating the corresponding split flux derivative. A second test that is used is based on an accuracy measurement. The idea of this test is that a "good" stencil must give accurate estimates of derivatives and vice versa. If the error in the computed derivatives is above some specified tolerance the stencil is classified as unacceptable. In this case we either enhance the stencil (to remove disc-type degenerate structure) or switch to full stencil. It is found that the full stencil almost always behaves well in terms of both the tests. The use of these two tests and the associated modifications of defective stencils in an automatic manner allows the solver to converge without any blow up. The results obtained for a 3-D configuration compare favorably with wind tunnel measurements and the framework developed here provides a rational basis for approaching the connectivity selection problem.
The second part of the thesis deals with a new scheme called Kinetic Meshless Method (KMM) which was developed as a consequence of the experience obtained with LSKUM and FAME mesh. As mentioned before the full stencil is generally better behaved than the split stencils. Hence the new scheme is constructed so that it does not require split stencils but operates on a full stencil (which is like a centered stencil). In order to obtain an upwind bias we introduce mid-point states (between a point and its neighbour) and the least squares fitting is performed using these mid-point states. The mid-point states are defined in an upwind-biased manner at the kinetic/Boltzmann level and moment-method strategy leads to an upwind scheme at the Euler level. On a standard 4-point Cartesian stencil this scheme reduces to finite volume method with KFVS fluxes. We can also show the rotational invariance of the scheme which is an important property of the governing equations themselves.
The KMM is extended to higher order accuracy using a reconstruction procedure similar to finite volume schemes even though we do not have (or need) any cells in the present case. Numerical studies on a model 2-D problem show second order accuracy. Some theoretical and practical advantages of using a kinetic formulation for deriving the scheme are recognized. Several 2-D inviscid flows are solved which also demonstrate many important characteristics. The subsonic test cases show that the scheme produces less numerical entropy compared to LSKUM, and is also better in preserving the symmetry of the flow. The test cases involving discontinuous flows show that the new scheme is capable of resolving shocks very sharply especially with adaptation. The robustness of the scheme is also very good as shown in the supersonic test cases.
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C, Praveen. "Development and Application of Kinetic Meshless Methods for Euler Equations." Thesis, Indian Institute of Science, 2004. http://hdl.handle.net/2005/154.
Full textAbstract:
Meshless methods are a relatively new class of schemes for the numerical solution of partial differential equations. Their special characteristic is that they do not require a mesh but only need a distribution of points in the computational domain. The approximation at any point of spatial derivatives appearing in the partial differential equations is performed using a local cloud of points called the "connectivity" (or stencil). A point distribution can be more easily generated than a grid since we have less constraints to satisfy.
The present work uses two meshless methods; an existing scheme called Least Squares Kinetic Upwind Method (LSKUM) and a new scheme called Kinetic Meshless Method (KMM). LSKUM is a "kinetic" scheme which uses a "least squares" approximation} for discretizing the derivatives occurring in the partial differential equations. The first part of the thesis is concerned with some theoretical properties and application of LSKUM to 3-D point distributions. Using previously established results we show that first order LSKUM in 1-D is positivity preserving under a CFL-like condition. The 3-D LSKUM is applied to point distributions obtained from FAME mesh. FAME, which stands for Feature Associated Mesh Embedding, is a composite overlapping grid system developed at QinetiQ (formerly DERA), UK, for store separation problems.
The FAME mesh has a cell-based data structure and this is first converted to a node-based data structure which leads to a point distribution. For each point in this distribution we find a set of nearby nodes which forms the connectivity. The connectivity at each point (which is also the "full stencil" for that point) is split along each of the three coordinate directions so that we need six split (or half or one-sided) stencils at each point. The split stencils are used in LSKUM to calculate the split-flux derivatives arising in kinetic schemes which gives the upwind character to LSKUM. The "quality" of each of these stencils affects the accuracy and stability of the numerical scheme. In this work we focus on developing some numerical criteria to quantify the quality of a stencil for meshless methods like LSKUM.
The first test is based on singular value decomposition of the over-determined problem and the singular values are used to measure the ill-conditioning (generally caused by a flat stencil). If any of the split stencils are found to be ill-conditioned then we use the full stencil for calculating the corresponding split flux derivative. A second test that is used is based on an accuracy measurement. The idea of this test is that a "good" stencil must give accurate estimates of derivatives and vice versa. If the error in the computed derivatives is above some specified tolerance the stencil is classified as unacceptable. In this case we either enhance the stencil (to remove disc-type degenerate structure) or switch to full stencil. It is found that the full stencil almost always behaves well in terms of both the tests. The use of these two tests and the associated modifications of defective stencils in an automatic manner allows the solver to converge without any blow up. The results obtained for a 3-D configuration compare favorably with wind tunnel measurements and the framework developed here provides a rational basis for approaching the connectivity selection problem.
The second part of the thesis deals with a new scheme called Kinetic Meshless Method (KMM) which was developed as a consequence of the experience obtained with LSKUM and FAME mesh. As mentioned before the full stencil is generally better behaved than the split stencils. Hence the new scheme is constructed so that it does not require split stencils but operates on a full stencil (which is like a centered stencil). In order to obtain an upwind bias we introduce mid-point states (between a point and its neighbour) and the least squares fitting is performed using these mid-point states. The mid-point states are defined in an upwind-biased manner at the kinetic/Boltzmann level and moment-method strategy leads to an upwind scheme at the Euler level. On a standard 4-point Cartesian stencil this scheme reduces to finite volume method with KFVS fluxes. We can also show the rotational invariance of the scheme which is an important property of the governing equations themselves.
The KMM is extended to higher order accuracy using a reconstruction procedure similar to finite volume schemes even though we do not have (or need) any cells in the present case. Numerical studies on a model 2-D problem show second order accuracy. Some theoretical and practical advantages of using a kinetic formulation for deriving the scheme are recognized. Several 2-D inviscid flows are solved which also demonstrate many important characteristics. The subsonic test cases show that the scheme produces less numerical entropy compared to LSKUM, and is also better in preserving the symmetry of the flow. The test cases involving discontinuous flows show that the new scheme is capable of resolving shocks very sharply especially with adaptation. The robustness of the scheme is also very good as shown in the supersonic test cases.
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Sanjose, Marlène. "EVALUATION DE LA METHODE EULER-EULER POUR LA SIMULATION AUX GRANDES ECHELLES DES CHAMBRES A CARBURANT LIQUIDE." Phd thesis, Institut National Polytechnique de Toulouse - INPT, 2009. http://tel.archives-ouvertes.fr/tel-00451199.
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Les turbines aéronautiques doivent satisfaire à des normes d'émissions polluantes toujours en baisse. La qualité du mélange du carburant et de l'air dans la chambre de combustion est responsable de la formation de polluants nocifs pour l'environnement. La simulation aux grandes échelles (LES) permet d'étudier les mécanismes de mélanges turbulents de l'air et du carburant. La prise en compte de l'aspect liquide du carburant injecté devient nécessaire pour prédire correctement l'apparition de vapeur de carburant au sein du foyer. Le but de cette thèse est évaluer la fiabilité des simulations LES Euler-Euler dans une configuration complexe. Les processus d'injection, et d'évaporation du carburant liquide sont analysés et modélisés dans les simulations LES car ils pilotent la formation de vapeur de carburant. Les méthodes numériques pour résoudre les équations continues de la phase dispersée doivent permettre des simulations précises et robustes dans une configuration représentative d'une chambre de combustion. Les simulations présentées dans ces travaux reproduisent l'écoulement diphasique évaporant non-réactif du banc d'essai Mercato. Ce banc est équipé d'un système d'injection d'air vrillé et d'un atomiseur pressurisé-swirlé de kérosène typiques des foyers aéronautiques réels. Dans ces travaux, le modèle pour l'injection de liquide FIM-UR a été développé pour définir les conditions limites conduisant à un spray issu d'un atomiseur préssurisé-swirlé. Le kérosène employé dans les campagnes expérimentales est modélisé dans les simulations par un composé permettant d'obtenir des temps d'évaporation réalistes. Trois stratégies numériques ont été mises en place sur la configuration MERCATO. Les comparaisons des résultats numériques aux mesures expérimentales ont permis d'évaluer la stratégie numérique conduisant à la meilleure précision. L'utilisation du schéma centré TTGC associé à un opérateur de viscosité artificielle localisée par un senseur adapté est optimale lorsque l'équation sur l'énergie décorrélée des gouttes est résolue. Cette stratégie permet de contrôler la localisation et les niveaux de viscosité par rapport à un schéma décentré. Les termes sources liés au mouvement mésoscopique permettent de redistribuer l'énergie dans les zones de compression ou de détente de la phase dispersée, et d'obtenir les bonnes répartitions des fluctuations dans la chambre de combustion. La stratégie retenue est comparée aux statistiques de la dynamique du spray résolu par une approche Lagrangienne employant la même injection monodispersse. Le méthode Euler-Euler conduit à la même précision de la dynamique de la phase dispersée que la méthode Euler-Lagrange. L'accès à l'évolution instationnaire de l'écoulement permet d'identifier les mêmes mécanismes de dispersion et de mélange dans les deux simulations. Des différences sur la répartition de diamètre moyen et de carburant dans la chambre ont été mis en évidence et reliés à la polydispersion locale qui n'est pas résolue dans l'approche Euler-Euler monodisperse et qui apparaît naturellement dans l'approche Euler-Lagrange malgré l'injection monodisperse.
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Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.
Full textAbstract:
A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton&<br>#8217<br>s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time.
In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude.
The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.
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Peters, Andreas [Verfasser], and Moctar Bettar Ould [Akademischer Betreuer] el. "Numerical Modelling and Prediction of Cavitation Erosion Using Euler-Euler and Multi-Scale Euler-Lagrange Methods / Andreas Peters ; Betreuer: Bettar Ould el Moctar." Duisburg, 2020. http://d-nb.info/1203066783/34.
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Luo, Luqing. "A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids." NCSU, 2010. http://www.lib.ncsu.edu/theses/available/etd-12032009-162626/.
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A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a polynomial solution of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting RDG method can be regarded as an improvement of a recovery-based DG method, in the sense that it shares the same nice features, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.
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Hanson, Christopher J. (Christopher John) 1971. "Integrated lifting-surface and Euler/boundary-layer theory analysis method for marine propulsors." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/91328.
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Thesis (Nav.E.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.<br>Includes bibliographical references (leaves 62-63).<br>by Christopher J. Hanson.<br>Nav.E.<br>S.M.
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Sekerci, Yadigar. "Some recent simulation techniques of diffusion bridge." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5749.
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<p>We apply some recent numerical solutions to diffusion bridges written in Iacus (2008). One is an approximate scheme from Bladt and S{\o}rensen (2007), another one, from Beskos et al (2006), is an algorithm which is exact: no numerical error at given grid points!</p>
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Böjeryd, Jesper. "Long Time Integration of Molecular Dynamics at Constant Temperature with the Symplectic Euler Method." Thesis, KTH, Numerisk analys, NA, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-165324.
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Simulations of particle systems at constant temperature may be used to estimate several of the system’s physical properties, and some require integration over very long time to be accurate. To achieve sufficient accuracy in finite time the choice of numerical scheme is important and we suggest to use the symplectic Euler method combined with a step in an Ornstein-Uhlenbeck process. This scheme is computationally very cheap and is often used in applications of molecular dynamics. This thesis strives to motivate the usage of the scheme due to the lack of theoretical results and comparisons to alternative methods. We conduct three numerical experiments to evaluate the scheme. The design of each experiment aims to expose weaknesses or strengths of the method. For both model problems and more realistic experiments are the results positive in favor of the method; the symplectic Euler method combined with an Ornstein- Uhlenbeck step does perform well over long times.<br>Simuleringar av partikelsystem vid konstant temperatur kan användas för att uppskatta flera av systemets fysiska egenskaper. Vissa klasser av egenskaper kräver integration över väldigt lång tid för att uppnå hög noggrannhet och för att uppnå detta i ändlig tid är valet av numerisk metod viktigt. Vi föreslår att använda den symplektiska Euler-metoden i kombination med ett implicit steg i en Ornstein-Uhlenbeck-process. Detta stegschema kräver låg beräkning jämfört med andra scheman och används redan i olika applikationer av molekyldynamik. Detta examensarbete eftersträvar att än mer motivera användandet av schemat, eftersom teoretiska resultat som stödjer metoder är få, och avsaknaden av tidigare liknande studier är betydlig. Vi genomför tre numeriska experiment för att pröva schemat. Under utformningen av experimenten har vi försökt att inkorporera olika fenomen som kan orsaka svårigheter för metoden för att exponera svagheter eller styrkor hos den. För båda modellproblem och för ett mer realistiskt experiment är resultaten positiva till schemats fördel; metoden att kombinera ett symplektisk Euler-steg med ett steg i Ornstein-Uhlenbeck-processen presterar bra över lång tid.
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PHAN, THI MY DUYEN. "Finite volume method for one-dimensional Euler equations and application to multi-fluid problem." Doctoral thesis, Gran Sasso Science Institute, 2021. http://hdl.handle.net/20.500.12571/23332.
Full textAbstract:
This thesis is about studying the finite volume method for hyperbolic conservation laws system. Starting from the one dimensional Euler equations, we rewrite them from the form in Eulerian coordinates into the form in the Lagrangian coordinates. This technique transforms a moving grid in Eulerian co- ordinates into a fixed grid in Lagrangian coordinates, thus allowing easier imple- mentation of boundary conditions.
The thesis consists of three parts:
• piston problem,
• multi-fluid models,
• asymptotic behavior of Euler equations.
In the first part, we consider the piston problem in the paper where the authors Yoshinori Inoue and Takeru Yano study the nonlinear propagation of plane waves radiated into a semi-infinite space filled with a perfect gas, by the sinusoidal motion of an infinite plate. They use the Euler equations in Eulerian coordinates describing the conservation of mass, momentum, and energy then approximate the solution. From this idea, we consider the waves propagating into a semi- infinite tube, which is filled with a perfect gas, closed by a piston on one end and extending along the x-axis at infinity. We use the mass Lagrangian coordinates to obtain the Euler equations rewritten in Lagrangian coordinates and reproduce the results following the piston problem in Yano's paper. The goal is to perform the computation in a finite computational domain, and to develop non-reflecting boundary conditions to impose on the right boundary. In order to reduce the impact of the reflected wave, we propose to combine the Burgers equation in few additional cells of the computational domain. The numerical error caused by the reflected wave is reduced by an order of magnitude by using this approach.
In the second part, we consider the tube filled periodically by a large number of pairs of two immiscible fluids. We use Roe’s solver, which is described in Munz's paper, in Lagrangian coordinates, to study the motion of multi-fluid problem and then compare this detailed numerical solution with two isentropic homogeneous models. The first one is a 2 × 2 isentropic system and the second model is a 3 × 3 system which takes into account some turbulent effects. The goal is to check which homogenized model gives better prediction. We study two cases according to the ratio of densities of the two fluids: moderate ratio and large ratio. For each case, we perform the test with smooth and discontinuous initial condition in pressure and velocity. For the problem with smooth initial conditions before the shock formation, the detailed numerical solutions and the numerical results of the two isentropic homogeneous models are in very good agreement. After the shock formation, the detailed numerical solution is strongly oscillatory and we have to use the average values, namely smoothed numerical solution, for the comparison with the two models. We observe the difference between the predictions of the two models. For moderate density ratio the 2×2 model gives a better prediction of the shock position, while for large density ratio, the turbulent 3×3 model is in better agreement with a smoothed out version of the detailed numerical solution compared with the simple 2 × 2 model.
In the third part, we study long time behavior of the solutions to the Euler equations by using two different numerical methods: the second order finite volume method in Lagrangian coordinates adopted in the previous chapters, and a high order finite volume method in Eulerian coordinate. In particular, the latter is based on WENO (Weighted Essentially Non-Oscillatory) reconstruction. Then we perform the comparison of the numerical solutions obtained at a final time, when pressure and velocity profiles are almost flat.
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Cretney, Rosanna Elizabeth. "Digitising Euler : 21st-century methods for the study of 18th-century mathematics." Thesis, Open University, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.700283.
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This thesis aims to introduce ideas and methods from the emerging field of digital humanities into the study of history of mathematics, through case studies relating to the role of correspondence, commu- nication, and collaboration in Leonhard Euler's mathematical practice. Euler's known correspondence numbers almost three thousand letters, exchanged with hundreds of correspondents from across Europe. The correspondence is a vital source for understanding Euler's mathem- atics, but it has not yet been examined in great detail; this thesis is a contribution towards such a study. The thesis is motivated by a case study which highlights the cent- ral role of correspondence and personal contact in Euler's work on continued fractions. A desire for better understanding of the corres- pondence leads to the use of methods from the digital humanities, a relatively young field which has been evolving rapidly since the begin- ning of the 21st century. The thesis considers the particular challenges encountered when using such methods in the study of eighteenth- century mathematical texts. A database is used to facilitate the explor- ation and comprehension of Euler's correspondence. This enables the identification of a corpus of letters, all connected with the same math- ematical topic, which would be suitable for further study. A prototype digital edition of one of these letters is presented, featuring a tran- scription, editorial annotations, and digital facsimiles of the original manuscript. Finally, it is shown how existing digital tools that were designed for use in other fields, such as mathematics and cartography, may be appropriated to aid understanding of primary sources in the history of mathematics.
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Paião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16806.
Full textAbstract:
Mestrado em Matemática e Aplicações<br>O Cálculo das Variações e o Controlo Ótimo são dois ramos da Matemática
que estão muito interligados entre si e também com outras áreas. Como
exemplo, podemos citar a Geometria, a Física, a Mecânica, a Economia, a
Biologia, bem como a Medicina. Nesta tese estudamos vários tipos de problemas
variacionais e de Controlo Ótimo, estabelecendo a ligação entre alguns
destes. Fazemos uma breve introdução sobre a Diabetes Mellitus, uma vez
que estudamos um modelo matemático que traduz a interação entre a glicose
e a insulina no sangue por forma a otimizar o estado de uma pessoa com
diabetes tipo 1.<br>The Calculus of Variations and the Optimal Control are two branches of Mathematics
that are very interconnected with each other and with other areas. As
example, we can mention Geometry, Physics, Mechanics, Economics, Biology
and Medicine. In this thesis we study various types of variational problems and
of Optimal Control, establishing the connection between some of these. We
make a brief introduction to the Diabetes Mellitus, because we study a mathematical
model that reflects the interaction between glucose and insulin in the
blood in order to optimize the state of a person with diabetes type 1.
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Ungun, Yigit. "Numerical Solution Of One Dimensional Detonation Tube With Reactive Euler Equations Using High Resolution Method." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614128/index.pdf.
Full textAbstract:
In this thesis, numerical simulation of one dimensional detonation tube problem is solved
with finite rate chemistry. For the numerical simulation, Euler equations have been used.
Since detonation tube phenomena occurs in high speed flows, viscosity eects and gravity
forces are negligible. In this thesis, Godunov type methods have been studied and afterwards
high resolution method is used for the numerical solution of the detonation tube problem. To
solve the chemistry aspect of the problem ZND theory have been used. For the numerical
solution, a FORTRAN code is written and the numerical solution of the problems compared
with the exact ZND solutions.
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Underwood, Tyler Carroll. "Performance Comparison of Higher-Order Euler Solvers by the Conservation Element and Solution Element Method." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1399017583.
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Ozdemir, Enver Doruk. "Implementation Of Rotation Into A 2-d Euler Solver." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606525/index.pdf.
Full textAbstract:
The aim of this study is to simulate the unsteady flow around rotating or oscillating airfoils. This will help to understand the rotor aerodynamics, which is essential in turbines and propellers.
In this study, a pre-existing Euler solver with finite volume method that is developed in the Mechanical Engineering Department of Middle East Technical University (METU) is improved. This structured pre-existing code was developed for 2-D internal flows with Lax-Wendroff scheme.
The improvement consist of firstly, the generalization of the code to external flow<br>secondly, implementation of first order Roe&rsquo<br>s flux splitting scheme and lastly, the implementation of rotation with the help of Arbitrary Lagrangian Eulerian (ALE) method.
For the verification of steady and unsteady results of the code, the experimental and computational results from literature are utilized. For steady conditions, subsonic and transonic cases are investigated with different angle of attacks. For the verification of unsteady results of the code, oscillating airfoil case is used.
The flow is assumed as inviscid, unsteady, adiabatic and two dimensional. The gravity is neglected and the air is taken as ideal gas.
The developed code is run on computers housed in METU Mechanical Engineering Department Computational Fluid Dynamics High Performance Computing (CFD-HPC) Laboratory.
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Jaegle, Félix. "LARGE EDDY SIMULATION OF EVAPORATING SPRAYS IN COMPLEX GEOMETRIES USING EULERIAN AND LAGRANGIAN METHODS." Phd thesis, Institut National Polytechnique de Toulouse - INPT, 2009. http://tel.archives-ouvertes.fr/tel-00452501.
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Dû aux efforts apportés à la réduction des émissions de NOx dans des chambres de combustion aéronautiques il y a une tendance récente vers des systèmes à combustion pauvre. Cela résulte dans l'apparition de nouveaux types d'injecteur qui sont caractérisés par une complexité géométrique accrue et par des nouvelles stratégies pour l'injection du carburant liquide, comme des systèmes multi-point. Les deux éléments créent des exigences supplémentaires pour des outils de simulation numériques. La simulation à grandes échelles (SGE ou LES en anglais) est aujourd'hui considérée comme la méthode la plus prometteuse pour capturer des phénomènes d'écoulement complexes qui apparaissent dans une telle application. Dans le présent travail, deux sujets principaux sont abordés: Le premier est le traitement de la paroi ce qui nécessite une modélisation qui reste délicate en SGE, en particulier dans des géométries complexes. Une nouvelle méthode d'implémentation pour des lois de paroi est proposée. Une étude dans une géométrie réaliste démontre que la nouvelle formulation donne de meilleurs résultats comparé à l'implémentation classique. Ensuite, la capacité d'une approche SGE typique (utilisant des lois de paroi) de prédire la perte de charge dans une géométrie représentative est analysée et des sources d'erreur sont identifiées. Le deuxième sujet est la simulation du carburant liquide dans une chambre de combustion. Avec des méthodes Eulériennes et Lagrangiennes, deux approches sont disponibles pour cette tâche. La méthode Eulérienne considère un spray de gouttelettes comme un milieu continu pour lequel on peut écrire des équations de transport. Dans la formulation Lagrangienne, des gouttes individuelles sont suivies ce qui mène à des équations simples. D'autre part, sur le plan numérique, le grand nombre de gouttes à traiter peut s'avérer délicat. La comparaison des deux méthodes sous conditions identiques (solveur gazeux, modèles physiques) est un aspect central du présent travail. Les phénomènes les plus importants dans ce contexte sont l'évaporation ainsi que le problème d'injection d'un jet liquide dans un écoulement gazeux transverse ce qui correspond à une version simplifiée d'un système multi-point. Le cas d'application final est la configuration d'un seul injecteur aéronautique, monté dans un banc d'essai expérimental. Ceci permet d'appliquer de manière simultanée tous les développements préliminaires de ce travail. L'écoulement considéré est non-réactif mais à part cela il correspond au régime ralenti d'un moteur d'avion. Dû aux conditions préchauffées, le spray issu du sstème d'injection multi-point s'évapore dans la chambre. Cet écoulement est simulé, utilisant les approaches Eulériennes et Lagrangiennes et les résultats sont comparés aux données expérimentales.
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CAMALET, EUGENE. "Methodes de couplage euler-lagrange pour les equations d'euler-poisson." Paris 6, 1995. http://www.theses.fr/1995PA066276.
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Nous etudions dans une premiere partie la modelisation d'un plasma froid par les equations d'euler-poisson sans pression. La description lagrangienne des equations de convection permet de prendre en compte les phenomenes de deferlement (vitesses multivoques) apparaissant dans ce type de plasma. Les instabilites dues a la methode particule/maille sont resorbees par l'introduction d'une pression numerique. La seconde partie est consacree a la simulation de dispositifs semiconducteurs de type mesfet et diode par un modele hydrodynamique isotherme. Les collisions sont modelisees par un terme de relaxation en temps. On utilise la methode numerique developpee dans la premiere partie. Enfin on etudie un modele sans pression ou la vitesse derive d'un potentiel couple a l'equation de poisson. Dans le cadre gravitationnel on montre que les solutions sont caracterisees par un principe de minimisation de l'energie. Si la densite est bornee on montre que les vitesses gagnent en regularite dans le cadre electrostatique et gravitationnel
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Carr, Elliot Joseph. "Exponential integrators and a dual-scale model for wood drying." Thesis, Queensland University of Technology, 2012. https://eprints.qut.edu.au/58742/1/Elliot_Carr_Thesis.pdf.
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For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions.
Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn.
For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid
ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore.
Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure.
Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic
ux to be defined as an average of the microscopic
ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.
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Temitayo, Emmanuel Olaosebikan [Verfasser]. "Application of the Euler-Lagrange-Method for solving optimal control problems : Research Work / Olaosebikan Temitayo Emmanuel." München : GRIN Verlag, 2019. http://d-nb.info/1199542520/34.
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Bailey, David A. "A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows." Thesis, University of Reading, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414620.
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Leobacher, Gunther, and Michaela Szölgyenyi. "Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient." Springer Nature, 2018. http://dx.doi.org/10.1007/s00211-017-0903-9.
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We prove strong convergence of order 1/4 - E for arbitrarily small E > 0 of
the Euler-Maruyama method for multidimensional stochastic differential equations
(SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is
based on estimating the difference between the Euler-Maruyama scheme and another
numerical method, which is constructed by applying the Euler-Maruyama scheme to
a transformation of the SDE we aim to solve.
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OH, JIYEON. "ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116256339.
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Cakmak, Mehtap. "Development Of A Multigrid Accelerated Euler Solver On Adaptively Refined Two- And Three-dimensional Cartesian Grids." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12610753/index.pdf.
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Cartesian grids offer a valuable option to simulate aerodynamic flows around complex geometries such as multi-element airfoils, aircrafts, and rockets. Therefore, an adaptively-refined Cartesian grid generator and Euler solver are developed. For the mesh generation part of the algorithm, dynamic data structures are used to determine connectivity information between cells and uniform mesh is created in the domain. Marching squares and cubes algorithms are used to form interfaces of cut and split cells. Geometry-based cell adaptation is applied in the mesh generation. After obtaining appropriate mesh around input geometry, the solution is obtained using either flux vector splitting method or Roe&rsquo<br>s approximate Riemann solver with cell-centered approach. Least squares reconstruction of flow variables within the cell is used to determine high gradient regions of flow. Solution based adaptation method is then applied to current mesh in order to refine these regions and also coarsened regions where unnecessary small cells exist. Multistage time stepping is used with local time steps to increase the convergence rate. Also FAS multigrid technique is used in order to increase the convergence rate. It is obvious that implementation of geometry and solution based adaptations are easier for Cartesian meshes than other types of meshes. Besides, presented numerical results show the accuracy and efficiency of the algorithm by especially using geometry and solution based adaptation. Finally, Euler solutions of Cartesian grids around airfoils, projectiles and wings are compared with the experimental and numerical data available in the literature and accuracy and efficiency of the solver are verified.
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Portas, Lance O. "An unstructured numerical method for computational aeroacoustics." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/16694.
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The successful application of Computational Aeroacoustics (CAA) requires high accuracy numerical schemes with good dissipation and dispersion characteristics. Unstructured meshes have a greater geometrical flexibility than existing high order structured mesh methods. This work investigates the suitability of unstructured mesh techniques by computing a two-dimensionallinearised Euler problem with various discretisation schemes and different mesh types. The goal of the present work is the development of an unstructured numerical method with the high accuracy, low dissipation and low dispersion required to be an effective tool in the study of aeroacoustics. The suitability of the unstructured method is investigated using aeroacoustic test cases taken from CAA Benchmark Workshop proceedings. Comparisons are made with exact solutions and a high order structured method. The higher order structured method was based upon a standard central differencing spatial discretisation. For the unstructured method a vertex-based data structure is employed. A median-dual control volume is used for the finite volume approximation with the option of using a Green-Gauss gradient approximation technique or a Least Squares approximation. The temporal discretisation used for both the structured and unstructured numerical methods is an explicit Runge-Kutta method with local timestepping. For the unstructured method, the gradient approximation technique is used to compute gradients at each vertex, these are then used to reconstruct the fluxes at the control volume faces. The unstructured mesh types used to evaluate the numerical method include semi-structured and purely unstructured triangular meshes. The semi-structured meshes were created directly from the associated structured mesh. The purely unstructured meshes were created using a commercial paving algorithm. The Least Squares method has the potential to allow high order reconstruction. Results show that a Weighted Least gradient approximation gives better solutions than unweighted and Green-Gauss gradient computation. The solutions are of acceptable accuracy on these problems with the absolute error of the unstructured method approaching that of a high order structured solution on an equivalent mesh for specific aeroacoustic scenarios.
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Helf, Clemens. "Eine Finite-Volumen-Methode in allgemeinen Zellen für die Euler-Gleichungen mit integrierter selbst-adaptiver Gittergenerierung." Stuttgart : Rechenzentrum, Univ. Stuttgart [u.a.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9832387.
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Yevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.
Full textAbstract:
This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the approximate stationary point converges in mean-square sense to the exact one as the time step of the numerical scheme diminishes.
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Stanescu, Dan. "Comparison of several numerical methods for solving the Euler equations for compressible aerodynamic flows." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22679.
Full textAbstract:
Two explicit time-integration schemes based on a finite-volume approach for the solution of the Euler equations are developed and used in the study of compressible flows. The starting point is a comparison of the performance of three widely used methods (i.e., Jameson's, MacCormack's and Godunov's) in several rather difficult test problems, characterized by the existence of flow discontinuities or strong nonlinearities. This indicates that the best solutions for such flows are obtained when the numerical method is closely related to the physical behaviour of the fluid, as is the case with Godunov's method, in contrast with the other two methods, which need a special treatment of the discontinuities, and are very prone to numerically induced oscillations. Therefore, a first scheme, which improves the way Jameson's method computes the flux-node variables in that it treats in a more realistic manner the physics of signal propagation in both subsonic and supersonic flow, is developed. The numerical experiments with this scheme suggest that it converges more rapidly and does not need the dissipation terms, thus leading to computer efficiency and a gain in accuracy. The second method is a linear hybrid, in conservative form, between MacCormack's and Godunov's methods, which is shown to keep the best features of both the methods: second order accuracy in smooth regions of the flow and lack of oscillations near discontinuities, where it behaves locally like a first-order monotone scheme.