Continuous compression waves in the two-dimensional Riemann problem

被引:0
作者
A. A. Charakhch’yan
机构
[1] Russian Academy of Sciences,Dorodnicyn Computing Center
来源
Computational Mathematics and Mathematical Physics | 2009年 / 49卷
关键词
shock waves; compression waves; shock wave reflection; Riemann problem; self-similar solution; gasdynamic equations;
D O I
暂无
中图分类号
学科分类号
摘要
The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.
引用
收藏
页码:1774 / 1780
页数:6
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