A homogeneous relaxation low Mach number model. (English) Zbl 1490.35312
Summary: 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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B50 | Maximum principles in context of PDEs |
| 35B09 | Positive solutions to PDEs |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 49M41 | PDE constrained optimization (numerical aspects) |
Keywords:
low Mach number flows; modelling of phase transition; relaxation model; HEM; HRM; analytical solutions; well-balanced scheme; asymptotic-preserving schemeReferences:
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