The two-dimensional Riemann problem in gas dynamics /
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 inte...
| Main Authors: | , , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
[Place of publication not identified] :
Routledge,
2022.
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| Edition: | First edition. |
| Series: | Pitman monographs and surveys in pure and applied mathematics,
no. 98 |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Physical Description: | 1 online resource (312 pages). |
| ISBN: | 9780203719138 0203719131 9781351408875 1351408879 9781351408882 1351408887 9781351408899 1351408895 |
| ISSN: | 0269-3666 ; |