Pressure-relaxation limit for a one-velocity Baer-Nunziato model to a Kapila model
Burtea C, Crin-Barat T, Tan J (2023)
Publication Type: Journal article
Publication year: 2023
Journal
DOI: 10.1142/S0218202523500161
Abstract
In this paper, we study a singular limit problem for a compressible one-velocity bifluid system. More precisely, we show that solutions of the Kapila system generated by initial data close to equilibrium are obtained in the pressure-relaxation limit from solutions of the Baer-Nunziato (BN) system. The convergence rate of this process is a consequence of our stability result. Besides the fact that the quasilinear part of the (BN) system cannot be written in conservative form, its natural associated entropy is only positive semi-definite such that it is not clear if the entropic variables can be used in the present case. Using an ad-hoc change of variables we obtain a reformulation of the (BN) system which couples, via low-order terms, an undamped mode and a non-symmetric partially dissipative hyperbolic system satisfying the Shizuta-Kawashima stability condition.
Authors with CRIS profile
Timothée Crin-Barat
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Additional Organisation(s)
Involved external institutions
Université Sorbonne Paris Cité
France (FR)
CY Cergy Paris University / CY Cergy Paris Université
France (FR)
France (FR)
CY Cergy Paris University / CY Cergy Paris Université
France (FR)
How to cite
APA:
Burtea, C., Crin-Barat, T., & Tan, J. (2023). Pressure-relaxation limit for a one-velocity Baer-Nunziato model to a Kapila model. Mathematical Models & Methods in Applied Sciences. https://dx.doi.org/10.1142/S0218202523500161
MLA:
Burtea, Cosmin, Timothée Crin-Barat, and Jin Tan. "Pressure-relaxation limit for a one-velocity Baer-Nunziato model to a Kapila model." Mathematical Models & Methods in Applied Sciences (2023).
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