Finite Difference Methods for the Stokes and Navier–Stokes Equations

Abstract

This paper presents a new finite difference scheme for the Stokes equations and incompressible Navier–Stokes equations for low Reynolds number. The scheme uses the primitive variable formulation of the equations and is applicable with nonuniform grids and nonrectangular geometries. Several other methods of solving the Navier–Stokes equations are also examined in this paper and some of their strengths and weaknesses are described. Computational results using the new scheme are presented for the Stokes equations for a region with curved boundaries and for a disk with polar coordinates. The results show the method to be second-order accurate.