A UNIFIED MULTIGRID SOLVER FOR THE NAVIER-STOKES EQUATIONS ON MIXED ELEMENT MESHES

A unified multigrid solution technique is presented for solving the Eu ler and Reynolds-averaged Navier-Stokes equations on unstructured mesh es using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms and tetrahedral in three dimensions. While the use of mixed elements is by no means a nov el idea, the contribution of the paper lies in the formulation of a co mplete solution technique which can handle structured grids, block str uctured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Na vier-Stokes equations on tetrahedral elements, and the thin layer vers ion of these equations on other types of elements, while using a singl e edge-based data-structure to construct the discretization over all e lement types. An agglomeration multigrid algorithm, which naturally ha ndles meshes of any types of elements, is employed to accelerate conve rgence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tet rahedral elements into quadrilateral or prismatic elements is also des cribed. The gains in computational efficiency afforded by the use of n on-simplicial meshes over fully tetrahedral meshes are demonstrated th rough several examples.