no. 4
A homogeneous relaxation low mach number model
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1569-1598

In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.

DOI : 10.1051/m2an/2021032
Classification : 35Q35, 35Q79, 65M25, 76T10
Keywords: Low Mach number flows, modelling of phase transition, relaxation model, HEM, HRM, analytical solutions, well-balanced scheme, asymptotic-preserving scheme 
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Faccanoni, Gloria; Grec, Bérénice; Penel, Yohan. A homogeneous relaxation low mach number model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1569-1598. doi: 10.1051/m2an/2021032

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