An efficient numerical method for solving the incompressible Navier-Stokes equations

Abstract

This paper describes an efficient numerical method for solving the steady incompressible Navier-Stokes equations. The method is a fully implicit method based on the generalized Galerkin method, and the resulting system of equations is solved in a sweeping mode by iterative line relaxation. Results of the present method are compared with published results for separating and reattaching flows, and parametric studies showing the effects of step size, boundary locations, and Reynolds number are presented. The present method is substantially faster than previously published methods; typical run times range from 10 sec to 1 min of 7600 CPU time; and, based on results obtained to date, it is stable at any Reynolds number.