Numerical Algorithms for Tracking Dynamic Fluid-Structure Interfaces in Embedded / Immersed Boundary Methods ∗

In any embedded/immersed boundary method, the embedded/immersed boundary needs to be tracked with respect to the non body-conforming Computational Fluid Dynamics (CFD) grid. When dealing with dynamic fluid-structure interaction problems with complex structural geometry, a robust, accurate, and efficient interface tracking algorithm becomes an important component of the computational framework. Existing methods developed in the CFD community have primarily focused on tracking closed boundaries with respect to uniform or non-uniform Cartesian CFD grids. In this work, two robust and efficient algorithms are presented for tracking embedded/immersed fluid-structure interfaces with respect to three-dimensional, arbitrary (i.e. structured or unstructured) CFD grids. First, a projection-based approach can be used when the interface is closed and fully resolved by the CFD grid, as it relies on the interface to separate the two distinct flow regimes “inside” and “outside” of it. When the surface is not closed, or is not fully resolved by the CFD grid, a slower but more general and accurate collision-based approach can be employed. Both approaches take advantage of a bounding box hierarchy to efficiently store and access the elements of the discretized interface. Moreover, for distributed flow computations, an algorithm for constructing distributed bounding box hierarchies is also presented. The performances of these algorithms are assessed in three-dimensional, dynamic fluid-structure interaction problems in the fields of aeronautics and underwater implosion. The differences between the two interface tracking algorithms in terms of capability, accuracy, and efficiency are revealed and discussed.