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| Two-Dimensional Riemann Problems for the Compressible Euler System |
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Citation： |
Yuxi ZHENG.Two-Dimensional Riemann Problems for the Compressible Euler System[J].Chinese Annals of Mathematics B,2009,30(6):845~858 |
| Page view： 1628
Net amount： 1268 |
Authors： |
Yuxi ZHENG; |
Foundation： |
the National Science Foundation (No. DMS-0603859). |
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| Abstract： |
Riemann problems for the compressible Euler system in two space dimensions
are complicated and difficult, but a viable alternative remains missing. The author lists
merits of one-dimensional Riemann problems and compares them with those for the cur-
rent two-dimensional Riemann problems, to illustrate their worthiness. Two-dimensional
Riemann problems are approached via the methodology promoted by Andy Majda in the
spirits of modern applied mathematics; that is, simplified model is built via asymptotic
analysis, numerical simulation and theoretical analysis. A simplified model called the
pressure gradient system is derived from the full Euler system via an asymptotic process.
State-of-the-art numerical methods in numerical simulations are used to discern small-
scale structures of the solutions, e.g., semi-hyperbolic patches. Analytical methods are
used to establish the validity of the structure revealed in the numerical simulation. The
entire process, used in many of Majda’s programs, is shown here for the two-dimensional
Riemann problems for the compressible Euler systems of conservation laws. |
Keywords： |
Characteristic decomposition, Guderley reflection, Hodograph transform,
Pressure gradient system, Self-similar, Semi-hyperbolic wave, Triple point
paradox, Riemann problem, Riemann variable |
Classification： |
35L65, 35J70, 35R35, 35J65 |
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