Immersed boundary methods have been widely used for simulating flows with complex geometries, as quality boundary-conforming 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.

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