A hybrid level set–front tracking finite element approach for fluid–structure interaction and two-phase flow applications

We present a hybrid level set–front tracking approach suitable for fluid–structure interaction and two-phase flow applications. Our approach aims at extending geometrical flexibility of standard mesh moving/front tracking methods by introducing an additional implicit level set representation of the geometry under consideration. The computational mesh is automatically aligned to the implicitly described geometry by minimizing a nonlinear, constrained functional. Resulting triangulations approximate the geometry accurately while being optimal in a certain sense. Due to the mesh alignment, finite element spaces defined on these triangulations may be easily adjusted to account for special solution properties such as discontinuities across interfaces. In order to demonstrate the flexibility of the proposed approach, we apply it to a simplified one-way coupled fluid–structure interaction problem inspired by the flow induced by a moving cardiac valve. Furthermore we evaluate the approach by solving a two-phase flow benchmark problem.