A Parallel Finite Element Discretization Scheme for the Natural Convection Equations

Abstract

This article presents a parallel finite element discretization scheme for solving numerically the steady natural convection equations, where a fully overlapping domain decomposition technique is used for parallelization. In this scheme, each processor computes independently a local solution in its subdomain using a mesh that covers the entire domain. It has a small mesh size h around the subdomain and a large mesh size H away from the subdomain. The discretization scheme is easy to implement based on existing serial software. It can yield an optimal convergence rate for the approximate solutions with suitable algorithmic parameters. Compared with the standard finite element method, the scheme is able to obtain an approximate solution of comparable accuracy with considerable reduction in computational time. Theoretical and numerical results show the promise of the scheme, where numerical simulation results for some benchmark problems such as the buoyancy-driven square cavity flow, right-angled triangular cavity flow and sinusoidal hot cylinder flow are provided.