Journal article
The cavitation and concentration of Riemann solutions for the isentropic Euler equations with isothermal dusty gas
Nonlinear analysis: real world applications, Vol.71, 103761
06/2023
DOI: 10.1016/j.nonrwa.2022.103761
Abstract
In this paper, we are mainly concerned with the phenomena of cavitation and concentration to the isentropic Euler equations with isothermal dusty gas as the pressure vanishes with double parameters. Firstly, we solve the Riemann problem by analyzing the properties of the elementary waves due to the existence of the inflection points. Secondly, we investigate the limiting behaviors of the Riemann solutions as the pressure vanishes and observe the cavitation and concentration phenomena. Finally, some numerical simulations are performed and the results are consistent with the theoretical analysis. The highlight of this paper is that we extend the restriction of ρθ≪1 in the previous works to ρθ<1, which makes the wave curve from convex to non-convex. And we prove that the limit of the Riemann solutions of isothermal dusty gas equations is the Riemann solutions of the limit of that equations as pressure vanishes, while the limiting process to vacuum state is different from the previous works.
Details
- Title: Subtitle
- The cavitation and concentration of Riemann solutions for the isentropic Euler equations with isothermal dusty gas
- Creators
- Weifeng JiangYuan Zhang - China Jiliang UniversityTong LiTingting Chen
- Resource Type
- Journal article
- Publication Details
- Nonlinear analysis: real world applications, Vol.71, 103761
- DOI
- 10.1016/j.nonrwa.2022.103761
- ISSN
- 1468-1218
- eISSN
- 1878-5719
- Language
- English
- Electronic publication date
- 10/2022
- Date published
- 06/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984339356402771
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