A homogeneous relaxation low mach number model
Copyright policy )A homogeneous relaxation low mach number model
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.
- Sorbonne Paris Cité France
- Panthéon-Assas University France
- Université de Toulon France
- Laboratoire Jacques-Louis Lions France
- Centre Inria de Paris France
relaxation model, Positive solutions to PDEs, asymptotic-preserving scheme, Asymptotic-preserving scheme, PDE constrained optimization (numerical aspects), PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, modelling of phase transition, well-balanced scheme, [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], PDEs in connection with classical thermodynamics and heat transfer, HEM, Liquid-gas two-phase flows, bubbly flows, Asymptotic behavior of solutions to PDEs, Modelling of phase transition, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Relaxation model, Maximum principles in context of PDEs, analytical solutions, Well-balanced scheme, low Mach number flows, Low Mach number flows, HRM
relaxation model, Positive solutions to PDEs, asymptotic-preserving scheme, Asymptotic-preserving scheme, PDE constrained optimization (numerical aspects), PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, modelling of phase transition, well-balanced scheme, [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], PDEs in connection with classical thermodynamics and heat transfer, HEM, Liquid-gas two-phase flows, bubbly flows, Asymptotic behavior of solutions to PDEs, Modelling of phase transition, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Relaxation model, Maximum principles in context of PDEs, analytical solutions, Well-balanced scheme, low Mach number flows, Low Mach number flows, HRM
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