Modeling hypersonic entry with the fully-implicit Navier–Stokes (FIN-S) stabilized finite element flow solver

• Implicit, stabilized FEM for modeling hypersonic flows including surface ablation.
• Choice of stabilization term τ critical for robustness of solve.
• Implemented using the libMesh finite element library to enhance robustness.
• Examples illustrate favorable comparison to established solvers, rapid convergence.
• Substantial savings compared to domain decomposition strategies for surface ablation.

In this paper, we present a novel scheme for modeling the hypersonic atmospheric entry of large vehicles with an ablative thermal protection system. The Favre-averaged thermochemical nonequilibrium Navier–Stokes equations with Spalart–Allmaras turbulence closure, thermodynamic, chemical kinetic, and quasi-steady ablation model are presented. The numerical method is based on a streamline upwind Petrov–Galerkin (SUPG) stabilized finite element formulation. The formulation and implementation of the finite element approximation are discussed in detail. The performance of the scheme is investigated through a series of increasingly complex applications, culminating in the simulation of a three-dimensional ablating heatshield in transitioning flow.