Two dimensional Riemann problem for a 2 × 2 system of hyperbolic conservation laws involving three constant states

Zhang and Zheng (1990) conjectured on the structure of a solution for a two-dimensional Riemann problem for Euler equation. To resolve this illuminating conjecture, many researchers have studied the simplified 2 × 2 systems. In this paper, 3-pieces Riemann problem for two-dimensional 2 × 2 hyperboli...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 321; pp. 49 - 62
Main Authors Hwang, Jinah, Shin, Myoungin, Shin, Suyeon, Hwang, Woonjae
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2018
Subjects
Conservation laws
Delta shock
Riemann problem
Conservation laws
76L15
Riemann problem
35L67
35L65
Delta shock
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Summary:Zhang and Zheng (1990) conjectured on the structure of a solution for a two-dimensional Riemann problem for Euler equation. To resolve this illuminating conjecture, many researchers have studied the simplified 2 × 2 systems. In this paper, 3-pieces Riemann problem for two-dimensional 2 × 2 hyperbolic system is considered without the restriction that each jump of the initial data projects one planar elementary wave. We classify twelve topologically distinct solutions and construct analytical and numerical solutions. The computed numerical solutions clearly confirm the constructed analytic solutions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.10.045