Application of an Iterative High Order Difference Scheme Along With an Explicit System Solver for Solution of Stream Function Vorticity Form of Navier–Stokes Equations

Abstract

This paper describes the general convectiondiffusion equation in 2D domain based on a particular fourth order finite difference method. The current fourthorder compact formulation is implemented for the first time, which offers a semiexplicit method of solution for the resulting equations. A nine point finite difference scheme with uniform grid spacing is also put into action for discretization purpose. The proposed numerical model is based on the Navier–Stokes equations in a stream functionvorticity formulation. The fast convergence characteristic can be mentioned as an advantage of this scheme. It combines the enhanced Fourniأ©'s fourth order scheme and the expanded fourth order boundary conditions, while offering a semiexplicit formulation. To accomplish this, some coefficients which do not influence the solutions are also omitted from Fourniأ©'s formulation. Consequently, very accurate results can be acquired with a relatively coarse mesh in a short time. The robustness and accuracy of the proposed scheme is proved using the benchmark problems of flow in a driven square cavity at medium and relatively high Reynolds numbers, flow over a backwardfacing step, and flow in an Lshaped cavity.