Development of numerical methods to simulate the melting of a thermal protection system

•Development of numerical methods to compute the ablation of metallic thermal protection system.•Extension of the operator splitting strategy to the five-equation model with dissipative effects.•Several approaches are detailed in order to prevent the numerical diffusion of the material interface in the transport step.•An ALE formulation of numerical schemes for both fluid and solid domains is given to capture accurately the melting front. In this paper, numerical methods are developed and detailed in order to be able to compute the ablation of metallic thermal protection system. In this complex multi-physics problem, the thermal state inside a solid domain and a two-phase viscous flow have to be computed. Since the two fluid phases are non-miscible, an extension of the five-equation model to dissipative effects is considered. An operator splitting strategy is used to separate the different phenomena according to their own propagation speed. An implicit time integration is performed for the acoustic+dissipative step while the transport step is computed with an explicit scheme. The hyperbolic part of the acoustic+dissipative step is solved in a non-conservative form using a Godunov-type scheme based on a simple Riemann solver. A classical discretization is used for the dissipative terms, and also for the heat equation inside the solid domain. Several approaches are detailed in order to prevent the numerical diffusion of the material interface in the transport step. Finally, since moving grids are used to capture accurately the melting front, an ALE formulation of the numerical schemes for both fluid and solid domains is given in a multidimensional framework. A fluid-solid coupling algorithm is then proposed to compute such a complex multi-physics problem. Numerical simulations show the validity and the robustness of the implicit-explicit scheme used for the discretization of the five-equation system. The last test case, namely the melting of an aluminium solid block by a lid-driven cavity filled with air, shows that the numerical tools developed here are robust enough to compute complex configurations involving a two-phase flow with high density ratios and a solid part.