Efficient Computation of Unsteady Viscous Flows by an Implicit Preconditioned Multigrid Method

An implicit preconditioned multigrid algorithm is developed for the efficient solution of two-dimensional, lowfrequency 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 the resolution requirements of the unsteady phenomena, 2) an inner preconditioned multigrid iteration that is explicit in pseudotime and rapidly convergent even in the presence of boundary-layer anisotropy, and 3) a compact stencil that is ideally suited for parallelization on distributed memory architectures. For fully resolved turbulent Navier-Stokes calculations of low-frequency pitching airfoils, the implicit discretization allows the use of time steps that are O(10) larger than are permissible with an explicit scheme. Convergence within the inner iteration is accelerated by a combination of blockJacobi preconditioning and J-coarsened multigrid to yield computational savings of roughly an order of magnitude over existing methods that rely on the standard combination of scalar time stepping and full-coarsened multigrid.