1. Two dimensional Riemann problem for a 2 × 2 system of hyperbolic conservation laws involving three constant states
- Author
-
Suyeon Shin, Woonjae Hwang, Jinah Hwang, and Myoungin Shin
- Subjects
Conjecture ,Geometric function theory ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Riemann's differential equation ,01 natural sciences ,Riemann solver ,010101 applied mathematics ,Riemann Xi function ,Riemann–Hurwitz formula ,Computational Mathematics ,symbols.namesake ,Riemann problem ,Riemann sum ,symbols ,0101 mathematics ,Mathematics - 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.
- Published
- 2018