NEW MULTIGRID APPROACH FOR 3-DIMENSIONAL UNSTRUCTURED, ADAPTIVE GRIDS

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by re distributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employ ed that uses the parent cells of the fine grid cells in an adapted mes h to generate successively coarser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlappi ng grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between th e independent grids. The solver is an explicit, vertex-based, finite v olume scheme that employs edge-based data structures and operations. S patial discretization is of central-differencing type combined with sp ecial upwind-like smoothing operators. Application cases include adapt ive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow arou nd the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.