A 2-D unsteady Navier-Stokes solution method with overlapping/overset moving grids

A simple, robust numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across 2-D, overset/overlapping, structured computational grids is presented. Overset/ overlapping grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The final parameters of the search algorithm give the interpolation weights at the interpolation point. The method is independent of numerical solution algorithms and it may easily be implemented on any 2-D, single block flow solver to make it a multi-block, zonal solver with arbitrarily overset/ overlapping computational grids. In the present study, numerical results are presented for steady and unsteady, viscous flow solutions over a flapping/stationary airfoil combination in tandem and over a single airfoil undergoing a sinusoidal flapping motion. The computational domains are discretized with overlapping and/or overset subgrids, which move in time relative to each other. The intergrid boundary point localization on the donor grid and the interpolation of flow variables are found to be accurate and robust. Computed flow variables are continuous across the grid boundaries and an excellent agreement is obtained against the single grid solutions