A local-relaxation method for solving convection-diffusion equations

Abstract

For constant-coefficient equations Young's SOR theory can be used to find an explicit formula for the optimum relaxation factor, even in cases when diagonal dominance is heavily violated. When desired simple approximations of ω_opt can be derived. Combining these with the LR strategy leads to a simple method which for varying coefficient equations, and for nonlinear equations, is able to outperform the optimum SOR method. The LR method can easily solve central-difference approximations of convection-diffusion equations, thus eliminating the need for the trade-off in favour of the upwind-type schemes mentioned in the introduction.