An adaptive semi-implicit scheme for simulations of unsteady viscous compressible flows

摘要

A numerical scheme for simulation of unsteady, viscous, compressible flows is considered. The scheme employs an explicit discretization of the inviscid terms of the Navier-Stokes equations and an implicit discretization of the viscous terms. The discretization is second order accurate in both space and time. Under appropriate assumptions, the implicit system of equations cna be decoupled into twolinear systems of reduced rank. These are solved efficiently usign a Gauss-Seidel method with multigrid convergence acceleration. When coupled with a solution adaptive mesh refinement technique, the hybrid explicit implicit scheme provides an effective methodology for accurate simulations of unsteady viscous flows. The methodology is demonstrated for both body-fitted structured grids and for rectangular (Cartesian) grids.