Accurate finite-difference methods for solving Navier-Stokes problems using Green's identities

Abstract

An investigation is presented of a method of numerical approximation to the steady-state Navier-Stokes equations in two space dimensions using the finite-difference methods of h⁴ accuracy recently published by Dennis and Hudson (1989) in conjunction with the global, or integral, methods based on Green's identities given by Dennis and Quartapelle (1989). It is shown that uniformly h⁴-accurate results can be obtained using this combination of methods without the necessity of making use of local approximations to the boundary vorticity. Some detailed results of computations are given for flow past a circular cylinder in the Reynolds number range 10–100 based on the diameter of the cylinder. The problem of flow in a square cavity in which one side is moved parallel to itself with constant velocity is also considered.