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

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

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)

FAU Profilzentrum Licht.Materie.Quantentechnologien (FAU LMQ) Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Université Sorbonne Paris Cité FR France (FR) CY Cergy Paris University / CY Cergy Paris Université FR 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://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).

BibTeX: Download