Robust and Efficient Setup Procedure for Complex Triangulations in Immersed Boundary Simulations

Immersed boundary methods have been widely used for simulating flows with complex geometries, as quality boundaryconforming grids are usually difficult to generate for complex geometries, especially, when motion and/or deformation is involved. Complex geometries can be conveniently represented using triangulated surfaces in a Lagrangian manner. A major task in immersed boundary simulations is to inject the immersed boundary information into the background Cartesian grid, such as the inside/outside status of a grid point with regard to the immersed boundary and the accurate sub-cell position of the immersed boundary for a grid point next to it. For high resolution simulations with moving/deforming boundaries, this step can be very expensive. In this paper, a simple, fast, and robust procedure is developed for setting up complex triangulations. Several cases with complex geometries are performed to demonstrate the efficiency and robustness.