Method Of Hyperbolic Systems With Stiff Relaxation PDF Download
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Total Pages | : |
Release | : 2001 |
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Download METHOD OF HYPERBOLIC SYSTEMS WITH STIFF RELAXATION. Book in PDF, ePub and Kindle
Three methods are analyzed for solving a linear hyperbolic system that contains stiff relaxation. We show that the semi-discrete discontinuous Galerkin method, with a linear basis, is accurate when the relaxation time is unresolved (asymptotically preserving--AP). A recently developed central method is shown to be non-AP. To discriminate between AP and non-AP methods, we argue that one must study problems that are diffusion dominated.
Author | : Richard Bissell Pember |
Publisher | : |
Total Pages | : 246 |
Release | : 1992 |
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Download Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation Book in PDF, ePub and Kindle
Author | : |
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Total Pages | : 5 |
Release | : 1999 |
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ISBN | : |
Download Discontinuous Galerkin for Hyperbolic Systems with Stiff Relaxation Book in PDF, ePub and Kindle
A Discontinuous Galerkin method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is unresolved, the method is accurate in the sense that it accurately represents the system's Chapman-Enskog approximation. Results are presented for the hyperbolic heat equation and coupled radiation-hydrodynamics.
Author | : Remi Abgrall |
Publisher | : Elsevier |
Total Pages | : 612 |
Release | : 2017-01-16 |
Genre | : Mathematics |
ISBN | : 044463911X |
Download Handbook of Numerical Methods for Hyperbolic Problems Book in PDF, ePub and Kindle
Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
Author | : Eliezer Guz |
Publisher | : |
Total Pages | : 99 |
Release | : 2011 |
Genre | : Differential equations, Hyperbolic |
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Download On Quasilinear Hyperbolic Systems with Stiff Relaxation Source Terms Book in PDF, ePub and Kindle
Author | : Thomas Y. Hou |
Publisher | : Springer Science & Business Media |
Total Pages | : 946 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642557112 |
Download Hyperbolic Problems: Theory, Numerics, Applications Book in PDF, ePub and Kindle
The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.
Author | : Jeffrey Alan Hittinger |
Publisher | : |
Total Pages | : 810 |
Release | : 2000 |
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Download Foundations for the Generalization of the Godunov Method to Hyperbolic Systems with Stiff Relaxation Source Terms Book in PDF, ePub and Kindle
Author | : Heinrich Freistühler |
Publisher | : Springer Science & Business Media |
Total Pages | : 527 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461201934 |
Download Advances in the Theory of Shock Waves Book in PDF, ePub and Kindle
In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
Author | : Edwige Godlewski |
Publisher | : Springer Nature |
Total Pages | : 846 |
Release | : 2021-08-28 |
Genre | : Mathematics |
ISBN | : 1071613448 |
Download Numerical Approximation of Hyperbolic Systems of Conservation Laws Book in PDF, ePub and Kindle
This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.
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Total Pages | : 10 |
Release | : 1999 |
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ISBN | : |
Download Discontinuous Galerkin for Stiff Hyperbolic Systems Book in PDF, ePub and Kindle
A Discontinuous Galerkin (DG) method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is under-resolved, DG is accurate in the sense that the method accurately represents the system's Chapman-Enskog (or ''diffusion'') approximation. Moreover, we demonstrate that a high-resolution, finite-volume method using the same time-integration method as DG is very inaccurate in the diffusion limit. Results for DG are presented for the hyperbolic heat equation, the Broadwell model of gas kinetics, and coupled radiation-hydrodynamics.