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

Abstract

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. 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 subcell position of the immersed boundary for a grid point next to it. Complex geometries in immersed boundary methods can be conveniently represented with triangulated surfaces placed upon underlying Cartesian grids in a Lagrangian manner. Regular, intuitive implementations using triangulations can be errorprone and/or cumbersome in dealing with robustness issues. In addition, they can be prohibitively expensive for high resolution simulations with complex moving/deforming boundaries. In this paper, a simple, robust, and fast procedure is developed for setting up complex triangulations in immersed boundary simulations. Central to this setup procedure are a ray casting and closest surface point computation algorithms. Several illustrative examples, including high resolution cases with Cartesian grids of up to 2.1 أ— 109 points and triangulations of up to 1.3 أ— 106 surface elements, are performed to demonstrate the robustness and efficiency of our procedure.