Approach for dynamic grids

The paper describes the development and application of a new multigrid method using adaptive-prismatic grids for viscous flow computations. The three-dimensional Navier-Stokes equations are solved on the prismatic grids that are adaptively refined locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributin g the changes in time of the solution from the fine grid to the coarser grids to accelerate convergence. The present approach uses the parent cells of the fine grid cells in an adapted mesh to generate successively coarser levels of multigrid. Furthermore, the prismatic grid is semi-unstruct ured and is constituted by layers of cells that are constructed from the triangulation on the surface of the body in a direction normal to the surface. This inherent structure of the prismatic grid is used in generating further coarser multigrid levels by deleting every other layer of cells. The solver is an explicit, vertex-based, finite volume scheme. Spatial discretization is of central-differencing type and temporal discretization is of Lax-Wendroff type. Application cases include adaptive solutions obtained with multigrid acceleration for flows with both shear layers and shock waves present. Convergence acceleration obtained by employing various levels of multigrid is investigated.