Numerical stability study of finite difference schemes for the resolution of three-dimensional time-dependent Navier-Stokes equations

Abstract

This paper is concerned with the numerical stability of two numerical schemes for the resolution of time-dependent three-dimensional Navier-Stokes equations. The numerical resolution is based on the finite difference method and the artificial compressibility method. The first computational scheme studied is semi-implicit of the Crank-Nicholson type. The second one is explicit. Necessary conditions of stability are given using the von Neumann test. Hence restrictions on relaxation factors in the case of the semi-implicit scheme and on the time step in the case of the explicit scheme are found.