Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and UnsteadyMultiscale Viscous Flows

Flows containing steady or nearly steady strong shocks on parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme, even under the multiblock grid or adaptive grid refinement framework. While sixthorder or higher-order shock-capturing methods are appropriate for unsteady turbulence with shocklets, third-order or lower shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. In order to minimize the short comings of low order and high order shock-capturing schemes for the subject flows, a multiblock overlapping grid with different types of spatial schemes and orders of accuracy on different blocks is proposed. The recently developed single block high order filter scheme in generalized geometries for Navier Stokes andmagnetohydrodynamics systems is extended to multiblock overlapping grid geometries. The first stage in validating the high order overlapping approach with several test cases is included. AMS subject classifications: 65Z05, 65M06, 65M50, 65M55, 65M60, 65M99, 65Y99