Integral vorticity transport method on an overset grid
We present an overset grid method for solution of the integro-differential vorticityvelocity formulation of the NavierStokes equations for two-dimensional, incompressible flow. The method uses a body-fitted inner grid, on which vorticity is evolved semi-implicitly, and a Cartesian outer grid with explicit vorticity evolution. The BiotSavart integral is solved using an adaptive, optimized multipole acceleration method. The BiotSavart integration is performed over all inner grid cells, over all active cells of the outer grid that lie entirely outside of the inner grid, and over sub-elements of a set of overhanging cells of the outer grid that overlap part of the inner grid. A novel method is developed using a level-set distance function to rapidly and easily partition the overhanging grid cells, which is essential for the BiotSavart integration in order to avoid double-counting vorticity in the overhanging region. A similar decomposition into outer, inner and overhanging cells is used in solving for pressure using a boundary-element formulation, which requires evaluation of an integral over the vorticity field using a method similar to that used for the BiotSavart integral. The new overset grid method is applied to flow past stationary and moving bodies in two dimensions and found to agree well with prior experimental and numerical results. Copyright (C) 2011 John Wiley & Sons, Ltd.
vorticity transport overset grids level-set function