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

Gloria Faccanoni (1) , Cédric 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.

Mots clés: phase change; Stefan problem; nonlinear degenerate diffusion

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Gloria Faccanoni, Cédric Galusinski. Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework. ESAIM: Proceedings and Surveys, 2023, Workshop on Compressible Multiphase Flows: Derivation, closure laws, thermodynamics, 72, pp.143-162. ⟨10.1051/proc/202372143⟩. ⟨hal-03872608v2⟩