A GMRES-Based Plane Smoother in Multigrid to Solve 3D Anisotropic Fluid Flow Problems

Abstract

For a discretization of the 3D steady incompressible Navier–Stokes equations a solution method is presented for solving flow problems on stretched grids. The discretization is a vertex-centered finite volume discretization with a flux splitting approach for the convective terms. Second-order accuracy is obtained with the well-known defect correction technique (B. Koren, J. Comput. Phys. 87, 25, 1990). The solution method used is multigrid, for which a plane smoother is presented for obtaining good convergence in flow domains with severely stretched grids. A matrix is set up in a plane, which is solved iteratively with a preconditioned GMRES method. Here, a stop criterion for GMRES is tested, which reduces the number of inner iterations compared to an “exact” plane solver without affecting the multigrid convergence rates. The performance of the solution method is shown for a Poisson model problem and for 3D incompressible channel flow examples.