The Two-Dimensional Riemann Problem in Gas Dynamics

Jiequan Li, Tong. Zhang, Shuli Yang (Academia Sinica, Beijing, China) , etc.

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English

CRC Press
21 August 1998

Differential & Riemannian geometry; Physics

Series: Monographs and Surveys in Pure and Applied Mathematics

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.

By: Jiequan Li, Tong. Zhang, Shuli Yang (Academia Sinica, Beijing, China), etc.
Imprint: CRC Press
Country of Publication: United Kingdom
Volume: 98
Dimensions: Height: 246mm, Width: 174mm, Spine: 23mm
Weight: 1.620kg
ISBN: 9780582244085
ISBN 10: 0582244080
Series: Monographs and Surveys in Pure and Applied Mathematics
Pages: 310
Publication Date: 21 August 1998
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

Li, Jiequan; Zhang, Tong.; Yang, Shuli