Efficient Treatment of Complex Geometries and Moving Bodies using Overlapping Grids

The overlapping grids method, also known as the Chimera method, is reviewed and discussed in the context of a methodology for the solution and analysis of flows around complex geometries and moving bodies. The overlapping grids method is a way of assembling multiple overlapping grids and treating them as a single grid that periodically update and exchange boundary information through proper interpolation in the regions where they meet. In this way, this method provides a flexible and efficient spatial discretization procedure for numerically solving PDEs on 2D or 3D domains. Topics to be addressed include the solution of the Navier-Stokes and Euler equations, in cases when the boundaries move according to a prescribed law of motion or when they remain fixed