On predicting incompressible flows by using a stabilized finite difference method with penalty

摘要

This paper presents a finite difference solution method for the incompressible Navier–Stokes equations, in primitive variables form. To provide the necessary coupling between continuity and momentum penalty method is introduced into continuity equation. Differential terms arising in Navier–Stokes equations are discretized by stabilized finite differences of the SU type (streamline upwind) to calculate the convective terms. The use of a penalty function method in a finite difference method of staggered grids, allows to eliminate the pressure and the result is a system of equations of the velocities arises. The aim of this paper is to describe the techniques used in the approximations to calculate each term of the discretized model. In particular, time integration techniques, solution of non-linearities associated to convective terms and constitutive laws, stabilization procedures and discretization of Navier–Stokes equation via finite differences are explained. Solving three standard fluid mechanics problems validates the method: the flow of a Newtonian fluid in a sudden contraction, the developing non-Newtonian fluid in a circular tube and a transient laminar axisymmetric flow trough a tube with a moderate local area reduction. Comparison with available experimental results is used to examine the accuracy of the method, reported a close agreement between the numerical prediction and the experimental data.