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

Author

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  • Hwang, Jinah
  • Shin, Myoungin
  • Shin, Suyeon
  • Hwang, Woonjae

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.

Suggested Citation

  • Hwang, Jinah & Shin, Myoungin & Shin, Suyeon & Hwang, Woonjae, 2018. "Two dimensional Riemann problem for a 2 × 2 system of hyperbolic conservation laws involving three constant states," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 49-62.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:49-62
    DOI: 10.1016/j.amc.2017.10.045
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    Cited by:

    1. Jinah Hwang & Suyeon Shin & Myoungin Shin & Woonjae Hwang, 2021. "Four-Quadrant Riemann Problem for a 2×2 System II," Mathematics, MDPI, vol. 9(6), pages 1-25, March.
    2. Jinah Hwang & Suyeon Shin & Myoungin Shin & Woonjae Hwang, 2021. "Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock," Mathematics, MDPI, vol. 9(2), pages 1-22, January.

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