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

• Published in: Computers & fluids Vol. 92; pp. 281 - 292
• Main Authors: Kirk, Benjamin S., Stogner, Roy H., Bauman, Paul T., Oliver, Todd A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 20.03.2014
• Subjects: Ablation; Compressible flow; Computer simulation; Finite element method; Fluid flow; Hypersonic flow; Mathematical analysis; Mathematical models; Navier-Stokes equations; Reentry; Stabilized finite elements; Surface ablation; Turbulent flow; Stabilized finite elements; Hypersonic flow; Reentry; Surface ablation; Compressible flow
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2013.10.003

•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.