Riemann problem for isentropic magnetogasdynamics in a variable cross‐section duct

In this paper, we mainly discuss the Riemann problem for conservation laws of isentropic magnetogasdynamics in a variable cross‐section duct. For any Riemann initial data, the existence of solution is obtained constructively in phase plane. The stability condition of stationary wave and the entropy...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2022-07, Vol.149 (1), p.266-292
Main Authors: Sheng, Wancheng, Xiao, Tao, Zhang, Qinglong
Format: Article
Language:English
Subjects:
Cauchy problems
Conservation laws
entropy rate admissibility criterion
Riemann problem for magnetogasdynamics in a variable cross‐section duct
stability condition of stationary wave
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Summary:In this paper, we mainly discuss the Riemann problem for conservation laws of isentropic magnetogasdynamics in a variable cross‐section duct. For any Riemann initial data, the existence of solution is obtained constructively in phase plane. The stability condition of stationary wave and the entropy rate admissibility criterion are postulated to guarantee the uniqueness of the Riemann solution. Our results can be applied to other conservation laws with similar geometric source terms without much difficulty. Moreover, the Riemann solutions have potential in the application to the design of numerical schemes in the future study.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12496