A homogeneous relaxation low mach number model

Abstract

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.

Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework

“…where x s κ are the transition points without diffusion defined in (9). We remark also that y s ℓ > x s ℓ if λ ℓ > 0.…”

“…This has promoted the development of so-called low Mach number models, which filter the sound waves. In the context of pressurized water reactor cores, an asymptotic low Mach number model, called lmnc (for Low Mach Nuclear Core), has been derived and investigated in a series of papers [1,2,4,5,[7][8][9]. The model was derived through an asymptotic expansion performed in the compressible Navier-Stokes equations with an energy source term.…”