Parallel, high-order overset grid implementation for supersonic flows

In this paper, a high-order, parallel overset grid solver is formulated for the solution of supersonic flows. The solver combines the Padé compact scheme with the weighted essentially nonoscillatory (WENO) scheme. The compact scheme provides high-order spatial differencing in smooth flows fields, while the WENO formulation is suited for flows containing discontinuities. The overset procedure for smooth flow fields uses high-order centered interpolation methods. For discontinuous fields, the selection of the stencil for interpolation follows the standard WENO procedure for spatial differencing. The developed procedure was validated using analytical test functions for both smooth and discontinuous fields. The interpolated values of the functions were compared with the known values of the function. The flux preservation property of the overset scheme was also verified. Applications including the flow past a circular cylinder and 3D sphere are presented for smooth flows. Supersonic flow over a cylinder at Mach number, Ma = 2.15 was also analyzed with the newly developed overset procedure. Results indicate superior performance of high-order interpolation compared to low order methods. In the presence of discontinuities, the shock-capturing high order interpolation procedure proposed in this paper performs better than procedures that use centered interpolation, particularly in the vicinity of discontinuities.