Recent advancements in fully implicit numerical methods for hypersonic reacting flows

In this paper we discuss a stabilized, continuous finite element scheme for chemically reacting flowfields in thermal nonequilibrium. This discrete formulation is solved using fully implicit algorithms, resulting in rapid convergence for steady-state applications, and robust convergence for problems with disparate time scales. The governing Reynolds-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, including recent enhancements in both the upwinding and shock capturing operators. Local mesh refinement is investigated as a technique for increasing accuracy in the vicinity of shockwaves, where the numerical method reverts to first-order accurate. 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.