An Accurate and Efficient Implicit Upwind Solver for the Navier-Stokes Equations

A new computer code for solving the Navier-Stokes equations for perfect gas and nonequilibrium flows is introduced. An unfactored implicit scheme has been developed which employs an efficient solution algorithm for the resulting system of linear equations. The nearly unrestricted stability of the scheme allows for large time steps and is therefore adequate for the resolution of the largely different time scales in complex viscous flow simulations. Small numerical dissipation is introduced in the calculation of the inviscid fluxes through the careful implementation of a Godunov-type upwind scheme which maintains uniform second order accuracy on locally skewed and stretched meshes. Results showing the accuracy and the convergence properties of this newly developed implicit Navier-Stokes solver are presented for inviscid and viscous channel and cascade flows.