Upwind differencing and LU factorization for chemical non-equilibrium navier-stokes equations

Abstract

An efficient and robust upwind method for solving the chemical non-equilibrium Navier-Stokes equations has been developed. The method uses either the Roe or Van Leer flux-splitting for inviscid terms and central differencing for viscous terms in the explicit operator (residual), and the Steger-Warming (SW) splitting and lower-upper (LU) approximate factorization for the implicit operator. This approach is efficient since the SW-LU combination requires the inversion of only block diagonal matrices, as opposed to the block tridiagonal inversion of the widely used ADI method, and is fully vectorizable. The LU method is particularly advantageous for systems with large number of equations, such as for chemical and thermal nonequilibrium flow. Formulas of the numerical method are presented for the finite-volume discretization of the Navier-Stokes equations in general coordinates. Numerical tests in hypersonic blunt body, ramped-duct, shock wave/boundary layer interaction, and divergent nozzle flows demonstrate the efficiency and robustness of the present method.