Cartesian Discretisations for Fluid-Structure Interaction - Efficient Flow Solver

The simulation of multiphysical scenarios has become a more and more important task of scientific computing within the last years. Due to their simplicity compared to monolithic approaches (solving a unique model for the whole scenario), partitioned approaches are widespread. They allow for a reusage of existing and established solvers for the involved physical phenomena such as fluid flow, structural mechanics, thermodynamics, etc. However, it is not trivial to correctly couple the single solvers and, in addition, to preserve the same efficiency as achieved for the single solvers. The reasons for efficiency drawbacks range from a numerically inefficient, possibly unstable coupling, costs of reimplementing coupling components for each couple of solvers (e.g. if MPCCI is used), communication costs, expensive search for neighbourhood relations between the grid points of the two solvers to inaccurate calculations of values exchanged at the coupling surface. We introduce an approach based on spacepartitioning grids that offer efficient solutions for many of the occuring problems both for the single solvers and for the coupling software in the context of fluid-structure interactions. For the coupling, we developed a client-server concept, that is a central coupling client is acting as a control unit of the coupled simulation. Such, we gained a high flexibility in terms of exchange of solvers. In this paper, we will not focus on the details of this coupling client, however, but on an efficient flow solver both as a stand-alone solver and in particular in the wider context of coupled simulations. To ensure robustness of the flow solver, we introduced a mass and energy preserving finite element discretisation on cartesian grids. On the basis of spacepartitioning grids in combination with space-filling curves, we established a very storage efficient implementation of the solver. For the algorithmic realisation of movements of the geometry, we use a marker-and-cell approach which is suitable for handling even very large defomations of the geometry as well as even topology changes. We implemented a fast algorithm to recreate the computational grid of the flow solver from the surface representation of the coupling client after each coupling step