An Implicit Multigrid Algorithm for Computing Hypersonic, Chemically Reacting Viscous Flows

Abstract

An implicit algorithm for computing viscous flows in chemical nonequilibrium is presented. Emphasis is placed on the numerical efficiency of the time integration scheme, both in terms of per-iteration workload and overall convergence rate. In this context, several techniques are introduced, including a stable,O(m2) approximate factorization of the chemical source Jacobian and implementations of V-cycle and filtered multigrid acceleration methods. A five species–seventeen reaction air model is used to calculate hypersonic viscous flow over a cylinder at conditions corresponding to flight at 5 km/s, 60 km altitude and at 11.36 km/s, 76.42 km altitude. Inviscid calculations using an eleven-species reaction mechanism including ionization are presented for a case involving 11.37 km/s flow at an altitude of 84.6 km. Comparisons among various options for the implicit treatment of the chemical source terms and among different multilevel approaches for convergence acceleration are presented for all simulations.