Primitive variable, pressure based flux-split, rns formulations for incompressible and compresible flows

摘要

Two primitive variable, pressure based flux-split RNS/NS solution procedures for viscous flows are presented. Both methods are valid across the full Mach number range, i.e., from the incompressible limit to high supersonic speeds. The first method is an "optimized" version of the previously developed global pressure relaxation RNS procedure. Considerabl reduction in the number of costly matrix inversions, and consequently in the computational time, is achieved. A speed up of almost 15 is attainable, as compared to the original procedure, for predominantly elliptic type flows. The second method is a time-marching, "linearized" convection RNS/NS procedure. The key to the efficiency of this procedure is the need for a single LU inversion at the inflow cross-plane. The remainder of the algorithm is based on simpel back-substitution. This method in the current form is not time-consistent and has a convective-only CFL type stability limitation. Both formulations are robust and provide accurate solutions for a variety of viscous flows.