Improving the stability and efficiency of the implicit pseudocompressibility method

The lower-upper symmetric Gauss-Siedel (LU-SGS) scheme, based on the pseudocompressibility method, is derived to the implicit method for compressible flows. The incompressible LU-SGS method is unconditionally stable and effective, but practices proves that the stability is affected by viscous Jacobians, especially for low-Reynolds-number flows. A viscous correction based on the incompressible Navier-Stokes equations with pseudocompressibility, based on the contribution of viscous Jacobians, improves the stability and efficiency. The Courant-Friedrichs-Lewy (CFL) number can be increased by stability analysis for simulation of low-Reynolds-number flow, considering the contributions of the viscous Jacobians. The numerical solution can be attained by the steady state with large CFL numbers, owing to improve stability, which is very useful for the incompressible simulation of low-Reynolds-number flows.