RNS Applications for Interacting Sub- and Supersonic Flows

Abstract

A solution based grid adaptation method that combines elements of the multigrid method for solution acceleration and the domain decomposition philosophy for grid optimization is described. Unlike other solution based adaptive gridding schemes, wherein the overhead of recomputing the grid and re-evaluating the solution on the adapted grid leads to higher computational costs compared to a non-adapted calculation, the present methodology reduces the computational time required to obtain the solution. The computational effort involved in the present calculation is significantly lower than a non-adapted calculation that utilizes the multigrid method purely as a convergence acceleration tool. In addition to convergence acceleration, the multigrid framework provides a mechanism of information transfer from regions wherein grid refinement is specified to unrefined coarse grid regions. The basis for domain decomposition in the current procedure is the variation in grid refinement requirements for each coordinate direction in different portions of the flow field. The method is demonstrated herein on an efficient set of governing equations termed the reduced Navier Stokes equations, applied in conjunction with a set of physical boundary conditions. The governing equations are discretized through a pressure based flux splitting procedure that is uniformly applicable from incompressible to supersonic Mach numbers.