Hole-cutting for three-dimensional overlapping grids

A hole-cutting technique for assembling overlapping grid systems for solving partial differential equations is presented. In the present method, the closed surfaces on the boundary of the three-dimensional computational domain are represented by hybrid surface grids. The hybrid grids are composed of nonoverlapping structured surface grids joined by an unstructured layer of triangles. Each hybrid grid is constructed from a subset of the physical boundary points on the faces of the component grids. The holes in the component grids are made by using a two-step mark-and-fill method. We first locate all grid cells that intersect the hybrid surface grids. We then apply the ray method to determine whether the grid points in these intersected grid cells are inside or outside the region bounded by the hybrid surface grids. As a result, the boundary of the hole region will be marked and it is a simple matter to then remove all points from the hole by starting from the outside points and traversing along all three grid directions until an inside point is found. To locate the intersecting grid cells, we employ the ray method augmented by an octree-based search technique together with Newton's method to invert the mappings corresponding to each component grid. We demonstrate the hole-cutting method by running the code Chalmesh to generate overlapping grids for a sphere in a box, around the stern of a ship, and around a three-bladed ship propeller.