Comparison of Numerical Methods for Solving the Convective-Diffusive Problem

Abstract

The convective-diffusive problem presents a challenge to several numerical methods. More efficientmethods are available when the problem is homogeneous. Three such methods are the boundary elementmethod (BEM), the boundary knot method (BKM), and the method of fundamental solutions (MFS). Thesemethods require only boundary nodes or boundary mesh, but not domain nodes or domain mesh as required bythe finite difference method or the finite element method. The performances of the three methods in solving asample two-dimensional convective-diffusive problem are compared in this paper. It is found that BKM and MFSgive more accurate results when the solution is a relatively smooth function, but fail when the solution varies toorapidly. On the other hand, BEM can deal with all types of solutions, and its solutions exhibit convergence.