eBook - ePub

The Two-Dimensional Riemann Problem in Gas Dynamics

Name: The Two-Dimensional Riemann Problem in Gas Dynamics
ISBN: 9781351408882

Jiequan Li,

Tong Zhang,

Shuli Yang,

312 pages
English
ePUB (mobile friendly)
Available on iOS & Android

eBook - ePub

The Two-Dimensional Riemann Problem in Gas Dynamics

Jiequan Li,

Tong Zhang,

Shuli Yang,

About this book

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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Yes, you can access The Two-Dimensional Riemann Problem in Gas Dynamics by Jiequan Li,Tong Zhang,Shuli Yang in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.