This paper addresses the numerical solution of a singularly perturbed two-dimensional convective-diffusion problem and the use of over-set (or overlapping or chimera) grids to solve the problem. The focus of the paper is the development of a clear analysis of approach and use of carefully developed overlapping grids to obtain accurate solutions and to determine the possibility of &egr;-uniform converge for singularly perturbed problems.

The paper provides a thorough introduction to overlapping grids and motivates the physical model problem and the use of a centered-differencing approach. The software used is OVERTURE, a C++ package developed at Lawrence Livermore National Laboratory. The overlapping grid is made up of a background domain, an annulus, and a strip through the domain. These grids are carefully analyzed for optimal priority in terms of grid generation. Numerical results are presented in both tabular and graphical form to clearly illustrate the simulated solution. While the question of convergence remains open, the paper points out that the uniform convergence is not demonstrated in the authors’ results thus far.