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Volume 9
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10.3390/math9020138
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Article

Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock

by
Jinah Hwang
1,
Suyeon Shin
1,
Myoungin Shin
2 and
Woonjae Hwang
1,*
1
Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea
2
Department of Ocean Systems Engineering, Sejong University, Seoul 05006, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(2), 138; https://doi.org/10.3390/math9020138
Submission received: 11 December 2020 / Revised: 4 January 2021 / Accepted: 7 January 2021 / Published: 10 January 2021
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
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Abstract

In this paper, a four-quadrant Riemann problem for a 2×2 system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.
Keywords: conservation laws; delta shock; 2-D Riemann problem conservation laws; delta shock; 2-D Riemann problem

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MDPI and ACS Style

Hwang, J.; Shin, S.; Shin, M.; Hwang, W. Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock. Mathematics 2021, 9, 138. https://doi.org/10.3390/math9020138

AMA Style

Hwang J, Shin S, Shin M, Hwang W. Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock. Mathematics. 2021; 9(2):138. https://doi.org/10.3390/math9020138

Chicago/Turabian Style

Hwang, Jinah, Suyeon Shin, Myoungin Shin, and Woonjae Hwang. 2021. "Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock" Mathematics 9, no. 2: 138. https://doi.org/10.3390/math9020138

APA Style

Hwang, J., Shin, S., Shin, M., & Hwang, W. (2021). Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock. Mathematics, 9(2), 138. https://doi.org/10.3390/math9020138

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