On a supersonic-sonic patch arising from the two-dimensional Riemann problem of the compressible Euler equations

Yanbo Hu, Guodong Wang
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Abstract

We are interested in the two-dimensional four-constant Riemann problem to the isentropic compressible Euler equations. In terms of the self-similar variables, the governing system is of nonlinear mixed-type and the solution configuration typically contains transonic and small-scale structures. We construct a supersonic-sonic patch along a pseudo-streamline from the supersonic part to a sonic point. This kind of patch appears frequently in the two-dimensional Riemann problem and is a building block for constructing a global solution. To overcome the difficulty caused by the sonic degeneracy, we apply the characteristic decomposition technique to handle the problem in a partial hodograph plane. We establish a regular supersonic solution for the original problem by showing the global one-to-one property of the partial hodograph transformation. The uniform regularity of the solution and the regularity of an associated sonic curve are also discussed.
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关于由可压缩欧拉方程的二维黎曼问题产生的超音速声波补丁
我们感兴趣的是等熵可压缩欧拉方程的二维四常数黎曼问题。就自相似变量而言,该治理系统属于非线性混合型,其解构型通常包含跨音速结构和小尺度结构。我们沿着从超音速部分到超声速点的伪流线构造了一个超音速-超声速补丁。这种补丁在二维黎曼问题中经常出现,是构建全局解的基石。为了克服声波退化带来的困难,我们应用特征分解技术来处理部分霍多图平面上的问题。通过证明部分霍多图变换的全局一一对应性质,我们建立了原始问题的正则超音速解。我们还讨论了解的均匀正则性和相关超声曲线的正则性。
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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
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The structure of finite groups whose elements outside a normal subgroup have prime power orders A unified characterization of convolution coefficients in nonlocal differential equations On a supersonic-sonic patch arising from the two-dimensional Riemann problem of the compressible Euler equations Dual formulation of constrained solutions of the multi-state Choquard equation Duality pairs, phantom maps, and definability in triangulated categories
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