Finite Difference Methods for the Stokes and Navier-Stokes Equations.

摘要

This paper presents a new finite difference scheme for the Stokes equations and incompressible Navier-Stokes equations for low Reynold's number. The scheme uses the primitive variable formulation of the equations and is applicable with non-uniform grids and non-rectangular 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 disc with polar coordinates. The results show the method to be second-order accurate. (Author)