Multigrid methods with skew-Hermitian based smoothers for the convection–diffusion problem with dominant convection

The convection–diffusion equation with dominant convection is considered on a uniform grid of central difference scheme. The multigrid method is used for solving the strongly nonsymmetric systems of linear algebraic equations with positive definite coefficient matrices. Two-step skew-Hermitian iterative methods are utilized for the first time as a smoothing procedure. It is demonstrated that using the proper smoothers enables to improve the convergence of the multigrid method. The robustness of the smoothers with respect to variation of the Peclet number is shown by local Fourier analysis and numerical experiments.