Vortex-Body Interaction using a Level-Set Based Overset Grid Method

An overset grid method is presented for solution of the integral vorticity-velocity formulation of the Navier-Stokes equations. The method uses an inner body-fitted grid and an outer Cartesian grid. The Biot-Savart integral is solved using an adaptive, optimized multipole acceleration method. The 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 level-set function is introduced in which the zero level-set curve coincides with the outer surface of the inner grid. This level-set function is used to rapidly subdivide the overhanging grid cells into triangular sub-cells which lie entirely outside of the inner grid, while omitting the parts of these cells that lie inside the inner grid, so as to avoid double-counting the vorticity in these regions. The pressure is solved as a post-processing variable using a boundary-element formation that requires evaluation of an integral using a parallel method to that used for velocity calculation. The method is applied to two-dimensional flow past stationary and moving bodies, and it is well suited to vortex-body interaction with complex, moving bodies.