The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation

Gauss-Seidel line relaxation is used to solve an implicit flux split difference approximation to the Navier-Stokes equations. The flux split approximation is chosen to maximize the weight of the diagonal elements of the block matrix elements that need to be inverted iteratively by the Gauss-Seidel procedure. There are several flux split approximations that can be chosen. However, not all are suitable for viscous flows containing shear or boundary layers. The present paper will illustrate the adverse effects of flux splitting in viscous flow calculations and propose corrections. The numerical procedures will be applied to solve for subsonic laminar flow past a flat plate, turbulent flow past a cone at March 6, and chemical and thermal nonequilibrium flow past a sphere-cone body at March 18.