An efficient finite-difference scheme for the steady incompressible Navier-Stokes equations using a curvilinear coordinate grid.

Abstract

An implicit time-marching finite-difference scheme for solving the steady incompressible Navier-Stokes equations is proposed. This scheme is based on the SMAC method for the curvilinear coordinate grid, where the delta-form approximate-factorization and the flux vector splitting techniques are applied, and some upstream-difference schemes and a staggered grid are also employed to suppress spurious error and numerical instabilities, especially for high Reynolds number flows. Numerical results for 2-D duct flow over a backward-facing step are shown, and compared with experimental data and existing numerical results to inspect the validity of the present scheme. The convergence rate to a steady state solution is improved several times in comparison with the explicit scheme, showing the present scheme to be very efficient.