Cartesian Discretisations for Fluid-Structure Interaction - Consistent Forces

Hierarchical Cartesian grids such as those defined by spacetrees have proven to be useful in lots of simulation scenarios in spite of their frequently supposed difficulties concerning the approximation of complicated and changing geometries. One of their most important advantages is the simple, efficient and flexible interface they offer. Thus, numerical single-field simulations can be embedded into some broader context as it is encountered in a partitioned solution approach to coupled or multi-physics problems in general and to fluid-structure interaction (FSI) in particular. For the latter, a flow solver, a structural solver, and a tool or library performing the data exchange and algorithmic interplay between the first two components are necessary. A reasonable trade-off between flexibility concerning the concrete codes used on the one hand and a satisfying overall efficiency on the other hand still remains an open challenge. This paper is dedicated to the generation and exchange of data on the fluid side for a partitioned approach to FSI, focusing on a strictly Cartesian, hierarchical grid. Details concerning the flow solver are discussed in another mini-symposium contribution [3]. Here, we report the design and implementation of the coupling environment realized as a client-server architecture that controls the coupling scheme and a discrete description of the geometry of the coupling surface. The solvers act as servers and respond to the client via a unique interface. Furthermore, we present the method of consistent forces proposed in [4], an elegant and efficient way for the calculation of stresses on Cartesian boundaries. We show how to use this method for both finite volume and finite element discretisations. A comparison of numerical results of the consistent forces with reference values of well-known benchmark scenarios shows the benefit this method can offer for the realisation of efficient FSI simulations