An HOC Finite Difference Scheme for the Steady Natural Convection Problem Based on the Velocity-Vorticity Method

Abstract

A high-order compact finite difference scheme for solving natural convection problems using velocity-vorticity formulation of the incompressible Navier-Stokes equations is presented. The basic idea of the method is to regard all controlling equations as the Poisson-type. We construct a fourth-order finite difference scheme for the velocity-vorticity equation based on the nine-point stencils for each Poisson-type equation. Next we give an example with an exact solution to verify that the scheme has the fourth-order accuracy. Finally, numerical solutions for the model problem of natural convection in a square heating cavity are presented to show the reliability and effectiveness of this method.