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

Jinah Hwang, Myoungin Shin, Suyeon Shin and Woonjae Hwang

Applied Mathematics and Computation, 2018, vol. 321, issue C, 49-62

Abstract: 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.

Keywords: Riemann problem; Conservation laws; Delta shock (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:321:y:2018:i:c:p:49-62

DOI: 10.1016/j.amc.2017.10.045

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