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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.
Produkteigenschaften
- Artikelnummer: 9780582244085
- Medium: Buch
- ISBN: 978-0-582-24408-5
- Verlag: Chapman and Hall/CRC
- Erscheinungstermin: 21.08.1998
- Sprache(n): Englisch
- Auflage: 1. Auflage 1998
- Serie: Monographs and Surveys in Pure and Applied Mathematics
- Produktform: Gebunden
- Gewicht: 1620 g
- Seiten: 310
- Format (B x H x T): 216 x 279 x 23 mm
- Ausgabetyp: Kein, Unbekannt