A note on an accelerated high-accuracy multigrid solution of the convection-diffusion equation with high Reynolds number

We present a new strategy to accelerate the convergence rate of a high-accuracy multigrid method for the numerical solution of the 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 an 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.