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

Gloria Faccanoni (1) , Cedric Galusinski (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate an advection-diffusion equation with a degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to a liquid-vapor mixture in the original model whereas the diffusion coefficient is non-degenerate in the pure phase cases. We focus on the influence of the diffusion coefficient on a simple 1D configuration for which some analytical computations can be done, leading to a surprising behavior of the phase transition with respect to the diffusion.

Keywords: phase change; Stefan problem; nonlinear degenerate diffusion

Domains: Analysis of PDEs [math.AP]; Numerical Analysis [math.NA]; Fluid mechanics [physics.class-ph]

Gloria Faccanoni, Cedric Galusinski. Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework. 2023. ⟨hal-03872608v2⟩