A multigrid solver for control-constrained Navier-Stokes control problems

Abstract

A multigrid solver for velocity tracking type control problems constrained by stationary Navier-Stokes equations is presented. Finite difference discretization is used on staggered grids. On these grids, a full multigrid method with coarsening by a factor-of-three strategy is proposed. For smoothing scheme, a distributive Gauss-Seidel scheme is used for the state and adjoint variables and a gradient update step for the control variable is applied. Numerical results validate the efficiency of the proposed multigrid algorithm.