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The Two Dimensional Riemann Problem In Gas Dynamics

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The Two Dimensional Riemann Problem In Gas Dynamics

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Author : Jiequan Li
language : en
Publisher: CRC Press
Release Date : 1998-08-21

The Two Dimensional Riemann Problem In Gas Dynamics written by Jiequan Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-21 with Mathematics categories.

The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.

The Two Dimensional Riemann Problem In Gas Dynamics

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Author : Jiequan Li
language : en
Publisher: Routledge
Release Date : 2022-02-13

The Two Dimensional Riemann Problem In Gas Dynamics written by Jiequan Li and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-13 with Mathematics categories.

The Riemann Problem For The Transportation Equations In Gas Dynamics

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Author : Wancheng Sheng
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

The Riemann Problem For The Transportation Equations In Gas Dynamics written by Wancheng Sheng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically

The Riemann Problem And Interaction Of Waves In Gas Dynamics

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Author : Tong Zhang
language : en
Publisher: Longman Scientific and Technical
Release Date : 1989

The Riemann Problem And Interaction Of Waves In Gas Dynamics written by Tong Zhang and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.

This monograph on shock wave theory contains much original work previously unpublished in the West covering the scalar conservation law, one-dimensional isothermal flow in an ideal gas, one-dimensional adiabatic flow, and two-dimensional flow (which is yet little understood). Includes 189 line drawings. Annotation copyrighted by Book News, Inc., Portland, OR

Hyperbolic Systems Of Conservation Laws

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Author : Philippe G. LeFloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-07-01

Hyperbolic Systems Of Conservation Laws written by Philippe G. LeFloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-01 with Mathematics categories.

This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

Multidimensional Hyperbolic Problems And Computations

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Author : James Glimm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Multidimensional Hyperbolic Problems And Computations written by James Glimm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

Combustion In High Speed Flows

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Author : John Buckmaster
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Combustion In High Speed Flows written by John Buckmaster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

This volume contains the proceedings of the Workshop on Com bustion, sponsored by the Institute for Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center (LaRC). It was held on October 12-14, 1992, and was the sec ond workshop in the series on the subject. The first was held in 1989, and its proceedings were published by Springer-Verlag under the title "Major Research Topics in Combustion," edited by M. Y. Hussaini, A. Kumar, and R. G. Voigt. The focus of the second workshop was directed towards the development, analysis, and application of basic models in high speed propulsion of particular interest to NASA. The exploration of a dual approach combining asymptotic and numerical methods for the analysis of the models was particularly encouraged. The objectives of this workshop were i) the genesis of models that would capture or reflect the basic pllysical phenomena in SCRAMJETs and/or oblique detonation-wave engines (ODWE), and ii) the stimulation of a greater interaction between NASA exper imental research community and the academic community. The lead paper by D. Bushnell on the status and issues of high speed propulsion relevant to both the SCRAMJET and the ODWE parallels his keynote address which set the stage of the workshop. Following the lead paper were five technical sessions with titles and chairs: Experiments (C. Rogers), Reacting Free Shear Layers (C. E. Grosch), Detonations (A. K. Kapila), Ignition and Struc ture (J. Buckmaster), and Unsteady Behaviour ('1'. L. Jackson).

Numerical Methods For Conservation Laws

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Author : LEVEQUE
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Numerical Methods For Conservation Laws written by LEVEQUE and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.

These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Front Tracking And Two Dimensional Riemann Problems Classic Reprint

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Author : James Glimm
language : en
Publisher: Forgotten Books
Release Date : 2017-11-23

Front Tracking And Two Dimensional Riemann Problems Classic Reprint written by James Glimm and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Science categories.

Excerpt from Front Tracking and Two Dimensional Riemann Problems A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reﬂection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Numerical Approximation Of Hyperbolic Systems Of Conservation Laws

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Author : Edwige Godlewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Numerical Approximation Of Hyperbolic Systems Of Conservation Laws written by Edwige Godlewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.

This work is devoted to the theory and approximation of nonlinear hyper bolic 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, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.

The Two Dimensional Riemann Problem In Gas Dynamics

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