Two-Dimensional Riemann Problem in Gas Dynamics
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A01=Jiequan Li
A01=Shuli Yang
A01=Tong. Zhang
advanced PDE solutions
Author_Jiequan Li
Author_Shuli Yang
Author_Tong. Zhang
Category=PBMP
Category=PH
Centred Rarefaction Wave
Characteristics
compressible flow analysis
conservation laws
delta shock theory
Delta-shocks
discontinuities
elementary waves
Entropy Condition
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eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
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Euler system
four-wave Riemann
Hyperbolic Conservation Laws
Hyperbolic Partial Differential Equations
mathematical fluid mechanics
multidimensional gas dynamics research
Non-convex Case
One-dimensional scalar
Ordinary Differential Equation
Planar elementary waves
Rankine Hugoniot Condition
Rankine Hugoniot Relation
Rarefaction Wave
Riemann Problem
Riemann Solutions
Scalar Conservation Laws
shock wave interaction
Singularity Curve
slip line dynamics
Vanishing Viscosity Method
Product details
- ISBN 9780582244085
- Weight: 1620g
- Dimensions: 174 x 246mm
- Publication Date: 21 Aug 1998
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
Li, Jiequan; Zhang, Tong.; Yang, Shuli
