High-order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high-order accurate, finite-difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier-Stokes equations. Fourth- or sixth-order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth-order accurate, centred finite differences. Implicit time marching is performed for both steady-state and time-accurate numerical solutions. High-order, spectral-type, low-pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non-linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright (C) 2004 John Wiley Sons, Ltd.