The Nitsche Method of the Navier-Stokes Equations for Immersed and Moving Boundaries

The usual way for a flow simulation with complex boundaries is to generate an unstructured mesh that represents the boundary accurately. In this classical approach, the generation and handling of the mesh is a complex t ask and the finite element method 1FEM} 011 unstructured meshes can generate significant computational overhead, especially in terms of memory requirements and access, an increasingly crucial aspect 011 massively parallel computing architectures. An alternative approach is the Immersed Boundary (IB! method. In this paper, we investigate the Nitsche Method for the Navier-Stokes equations (NSE) with immersed boundaries. This method avoids the usage of computationally costly unstructured meshes by using an adaptive Cartesian mesh instead. In contrast to unstructured meshes, Cartesian meshes can be partitioned in a load-balanced way without a central storage of the whole mesh information and are highly storage efficient even in a sequential context. For an accurate simulation of our scenarios, no-slip boundary conditions need to be imposed on complex boundary, that is not represented by the mesh facets. For this purpose, we employ the Nitsche Method to impose these conditions in a weak form. We extend the approach for moving boundaries, which enables us to compute fluid-structure interaction (FSI) scenarios. The results of various FSI benchmark scenarios, presented at the end of this paper, verify our approach.