| The Two-Dimensional Riemann Problem in Gas Dynamics Contributor(s): Li, Jiequan (Author), Zhang, Tong (Author), Yang, Shuli (Author) |
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ISBN: 0582244080 ISBN-13: 9780582244085 Publisher: CRC Press OUR PRICE: $218.50 Product Type: Hardcover - Other Formats Published: August 1998 |
| Additional Information |
| BISAC Categories: - Science | Physics - Mathematical & Computational - Science | Mechanics - Dynamics - Mathematics | Applied |
| Dewey: 533.2 |
| LCCN: 00000000 |
| Series: CRC Monographs and Surveys in Pure and Applied Math (Hardcover) |
| Physical Information: 0.89" H x 6.3" W x 9.44" (1.28 lbs) 310 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |