A Conservative Two-Phase Flow Model With a Nonlinear Degenerate Diffusion

This paper is motivated by the need to model the dynamics of liquid-vapor flows involving phase transitions in heat exchangers. In the low Mach number asymptotic limit, we derive a system of 1D conservation laws with heat transfers causing phase change, with a degenerate and nonlinear thermal diffusion coefficient. This degeneracy induces discontinuities on the solution, both on the enthalpy and the velocity. We provide explicit steady and traveling wave solutions, and derive suitable numerical schemes able to capture the moving discontinuities.