Multidimensional transonic shock waves and free boundary problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-21 DOI:10.1142/S166436072230002X

Gui-Qiang G. Chen, M. Feldman

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引用次数: 5

Abstract

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic–hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection–diffraction, and the Prandtl–Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs.

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多维跨音速激波与自由边界问题

本文讨论了可压缩流体力学中欧拉方程在分析多维跨音速激波时所引起的自由边界问题。本文综述了在多维跨音速激波分析和相应的可压缩欧拉方程及相关的混合型非线性偏微分方程的自由边界问题方面的一些最新进展。本文分析的非线性偏微分方程包括定常势流欧拉方程、定常全欧拉方程、定常势流欧拉方程以及相关的混合椭圆-双曲型非线性偏微分方程。跨声速激波问题包括稳定跨声速流过固体楔块的问题、激波反射-衍射的冯·诺依曼问题和非定常超音速流过固体楔块的prandtle - meyer问题。我们首先展示了如何将这些长期存在的多维跨音速激波问题表述为可压缩欧拉方程和相关的混合型非线性偏微分方程的自由边界问题。然后给出了求解这些自由边界问题的一种有效的非线性方法及相关思想和技术。该方法、思想和技术将有助于分析其他长期存在的和新出现的非线性偏微分方程的自由边界问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.