A Note on Accelerated High Accuracy Multigrid Solution of
Convection-Diffusion Equation with High Reynolds Number

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


We present a new strategy to accelerate the convergence rate of a high accuracy multigrid method for the numerical solution of convection-diffusion equation at the high Reynolds number limit. We propose a scaled residual injection operator with a scaling factor proportional to the magnitude of the convection coefficients, an alternating line Gauss-Seidel relaxation, and a minimal residual smoothing acceleration technique for the multigrid solution method. The new implementation strategy is tested to show improved convergence rate with three problems, including one with a stagnation point in the computational domain. The effect of residual scaling and the algebraic properties of the coefficient matrix arising from the fourth order compact discretization are investigated numerically.

Key words}: Multigrid method, fourth order compact discretization schemes, residual transfer operators, convection-diffusion equation.

This paper has been published in Numerical Methods for Partial Differential Equations, Vol. 6 (1), 1-10, 2000.