DIRECTIONAL VISCOUS MULTIGRID USING ADAPTIVE PRISMATIC MESHES

The paper describes the development and application of a new multigrid method using adaptive-prismatic grids for viscous now computations. T he three-dimensional Navier-Stokes equations are solved on the prismat ic grids that are adaptively refined locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redist ributing the changes in time of the solution from the fine grid to the coarser grids to accelerate convergence. The present approach uses th e parent cells of the fine grid cells in an adapted mesh to generate s uccessively coarser levels of multigrid. Furthermore, the prismatic gr id is semi-unstructured and is constituted by layers of cells that are constructed from the triangulation on the surface of the body in a di rection normal to the surface. This inherent structure of the prismati c grid is used in generating further coarser multigrid levels by delet ing every other layer of cells. The solver is an explicit, vertex-base d, finite volume scheme. Spatial discretization is of central-differen cing type and temporal discretization is of Lax-Wendroff type. Applica tion cases include adaptive solutions obtained with multigrid accelera tion for flows with both shear layers and shock waves present. Converg ence acceleration obtained by employing various levels of multigrid is investigated.