Numerical simulation of natural convection in a square cavity using vorticity-velocity formulation.

Abstract

Two-dimensional incompressible Navier-Stokes equations in vorticity-velocity formulation and the energy equation for temperature have been solved using a method of lines approach. The spatial derivatives are discretized by means of the central finite differential approximation, and the resulting system of the ordinary differential equations in time is integrated by a rational Runge-Kutta (RRK)scheme. Poisson equations for velocity are solved by a Group Explicit Iterative (GEI) method, using the multigrid technique. The GEI method is a fully explicit scheme so it takes advantage of the supercomputer's architecture. As the verification of the scheme, the classical problem of natural convection in a square cavity of Boussinesq fluid has chosen. Numerical calculations are obtained at a Prandtle number of 0.71 corresponding to air and Rayleigh number up to 108. The results of calculation essentially agree well with those of de Vahl Davis.