Data transfer strategies for overset and hybrid computational methods

Abstract

Modern computational science permits the accurate solution of nonlinear partial differential equations (PDEs) on overlapping computational domains, known as an overset approach. The complex grid interconnectivity inherent in the overset method can introduce errors in the solution through “orphan” points, i.e., grid points for which reliable solution donor points cannot be located. For this reason, a variety of data transfer strategies based on scattered data interpolation techniques have been assessed with application to both overset and hybrid methodologies. Scattered data approaches are attractive because they are decoupled from solver type and topology, and may be readily applied within existing methodologies. In addition to standard radial basis function (RBF) interpolation, a novel steered radial basis function (SRBF) interpolation technique has been developed to introduce data adaptivity into the data transfer algorithm. All techniques were assessed by interpolating both continuous and discontinuous analytical test functions. For discontinuous functions, SRBF interpolation was able to maintain solution gradients with the steering technique being the scattered-data analog of a slope limiter. In comparison with linear mappings, the higher-order approaches were able to more accurately preserve flow physics for arbitrary grid configurations. Overset validation test cases included an inviscid convecting vortex, a shock tube, and a turbulent ship airwake. These were studied within unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations to determine quantitative and qualitative improvements when applying RBF interpolation over current methods. The convecting vortex was also analyzed on a grid configuration which contained orphan points under the state-of-the-art overset paradigm. This was successfully solved by the RBF-based algorithm, which effectively eliminated orphans by enabling high-order extrapolation. Order-of-magnitude reductions in error compared to the exact vortex solution were observed. In addition, transient conservation errors that persisted in the original overset methodology were eliminated by the RBF approach. To assess the effect of advanced mapping techniques on the fidelity of a moving grid simulation, RBF interpolation was applied to a hybrid simulation of an isolated wind turbine rotor. The resulting blade pressure distributions were comparable to a rotor simulation with refined near-body grids.