A hybrid time-stepping method of local preconditioning on high aspect ratio grids

Time-derivative preconditioning methods have provided robust convergences and accurate solutions for low-speed inviscid flows by using local flow properties as the reference scaling parameter in the preconditioning matrix. During viscous or turbulent flow calculations, the use of high aspect ratio grids to obtain accurate solutions near the wall often results in stiff convergence and nonphysical solutions in the singular regions. In this paper, a switching method is proposed as a remedy to that problem by combining the advantages of the typical local time-stepping and min-CFL/max-VNN methods. The proposed method is based on results of our study of the inviscid bump flow and flat plate boundary layer flows and also proved to be effective to a turbulent flow simulation around the NACA 4412 airfoil.