Multigrid Algorithm for Computing Hypersonic, Chemically Reacting Flows

Abstract

A robust and efficient multigrid method for computing inviscid and viscous high-speed steady-state reactive flows is presented. Curve-fitted data are used to calculate equilibrium properties. Nonequilibrium flows are calculated using five-species and two-temperature air models. The advection upstream splitting method by pressure-based weight functions is used to acquire robustness and spatial accuracy in capturing a shock and resolving a boundary layer. The five-stage Runge– Kutta and lower-upper symmetric Gauss– Seidel schemes are adopted for efficient time integration. The chemical source terms are treated in a point-implicit manner when five-stage Runge– Kutta is used. To overcome the stability problem in applying the multigrid method to high-speed reactive flow calculations, a modified damped prolongation and a new implicit residual smoothing are proposed. The proposed methods are applied to the computations of hypersonic equilibrium and nonequilibrium flows over a half-cylinder. The results reveal the robustness of the proposed methods and substantial multigrid speed-ups in both the equilibrium and nonequilibrium test cases.