Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid

Tingting Chen; Weifeng Jiang; Tong Li; Zhen Wang; Junhao Lin

doi:10.3390/math12162444

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Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid

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Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid

Tingting Chen, Weifeng Jiang, Tong Li, Zhen Wang and Junhao Lin

Mathematics (Basel), Vol.12(16), 2444

08/06/2024

DOI: 10.3390/math12162444

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Abstract

We are concerned with the Riemann problem for the isentropic Euler equations of mixed type in the dark energy fluid. This system is non-strictly hyperbolic on the boundary curve of elliptic and hyperbolic regions. We obtain the unique admissible shock waves by utilizing the viscosity criterion. Assuming fixed left states are in the elliptic and hyperbolic regions, respectively, we construct the unique Riemann solution for the mixed-type models with the initial right state in some feasible regions. Finally, we present numerical simulations which are consistent with our theoretical results.

conservation laws

Riemann problem

mixed type

shock waves

Details

Title: Subtitle: Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid
Creators: Tingting Chen - Jianghan University
Weifeng Jiang - China Jiliang University
Tong Li - University of Iowa
Zhen Wang - Wuhan University of Technology
Junhao Lin - China Jiliang University
Resource Type: Journal article
Publication Details: Mathematics (Basel), Vol.12(16), 2444
Publisher: MDPI
DOI: 10.3390/math12162444
ISSN: 2227-7390
eISSN: 2227-7390
Grant note: Natural Science Foundation of Zhejiang: LQ18A010004 Subproject of Key Scientific Research Project of Zhejiang Provincial Department of Transportation: G92N-1003-21 National Natural Science Foundation of China: 11771442
The research of Weifeng Jiang is supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang (Grant No. 2021YW39), the Natural Science Foundation of Zhejiang (Grant No. LQ18A010004), the Subproject of Key Scientific Research Project of Zhejiang Provincial Department of Transportation (Grant No. G92N-1003-21). The research of Zhen Wang is supported by the National Natural Science Foundation of China (Grant No. 11771442).
Language: English
Date published: 08/06/2024
Academic Unit: Mathematics
Record Identifier: 9984696701902771

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