EFFICIENT COMPUTATION OF UNSTEADY VISCOUS FLOWS BY AN IMPLICIT PRECONDITIONED MULTIGRID METHOD

An implicit preconditioned multigrid algorithm is developed for the ef ficient solution of two-dimensional, low-frequency unsteady turbulent Navier-Stokes calculations on highly stretched meshes. The efficiency of the approach derives from three key attributes: 1) an implicit time discretization that allows the time step to be determined solely by t he resolution requirements of the unsteady phenomena, 2) an inner prec onditioned multigrid iteration that is explicit in pseudotime and rapi dly convergent even in the presence of boundary-layer anisotropy, and 3) a compact stencil that is ideally suited for parallelization on dis tributed memory architectures. For fully resolved turbulent Navier-Sto kes calculations of tow frequency pitching airfoils, the implicit disc retization allows the use of time steps that are O(10(6)) larger than are permissible with an explicit scheme. Convergence within the inner iteration is accelerated by a combination of block-Jacobi precondition ing and J-coarsened multigrid to yield computational savings of roughl y an order of magnitude over existing methods that rely on the standar d combination of scalar time stepping and full-coarsened multigrid.