Four-Quadrant Riemann Problem for a 2×2 System II

Jinah Hwang, Suyeon Shin, Myoungin Shin and Woonjae Hwang
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Jinah Hwang: Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea
Suyeon Shin: Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea
Myoungin Shin: Department of Ocean Systems Engineering, Sejong University, Seoul 05006, Korea
Woonjae Hwang: Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea

Mathematics, 2021, vol. 9, issue 6, 1-25

Abstract: In previous work, we considered a four-quadrant Riemann problem for a 2 × 2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In this paper, we consider the case that does not involve a delta shock at the initial discontinuity. We classified 18 topologically distinct solutions and constructed analytic and numerical solutions for each case. The constructed analytic solutions show the rich structure of wave interactions in the Riemann problem, which coincide with the computed numerical solutions.

Keywords: Riemann problem; conservation laws; hyperbolic system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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