On local-relaxation methods and their application to convection-diffusion equations

A local relaxation (LR) method, based on successive over-relaxation (SOR) theory, is presented. The performance of LR methods is illustrated by applying them to central-difference approximations of convection-diffusion equations. It is found that equations with small diffusion coefficients can be handled without difficulty. For equations with strongly-varying coefficients, and for nonlinear equations, an LR method can be significantly more efficient than the optimum SOR method. For example, a 16 x 16 driven-cavity problem for a Reynolds number of one million can be solved in just a few seconds on a CDC 6600 computer.