CARTESIAN DISCRETISATIONS FOR FLUID-STRUCTURE INTERACTION { CONSISTENT FORCES

Hierarchical Cartesian grids such as those dene d by spacetrees have proven to be useful in lots of simulation scenarios in spite of their frequently supposed diculties concerning the approximation of complicated and changing geometries. One of their most important advantages is the simple, ecient and exible interface they oer. This provides the possibility to embed numerical single-eld simulations into some broader context as it is encountered in a partitioned solution approach to coupled or multi-physics problems in general and to uid-structur e interaction (FSI) in particular. For the latter, a ow solver, a structural solver, and a tool or library performing the data exchange and algorithmic interplay between the rst two components are necessary. A reasonable trade-o between exibility concerning the concrete codes used on the one hand and a satisfying overall eciency on the other hand still remains an open challenge. This paper addresses the generation and exchange of data on the uid side for a par- titioned approach to FSI, focusing on a strictly Cartesian, hierarchical grid. The details concerning the ow solver are discussed in a second contribution (6). We report the de- sign and implementation of the coupling environment and present an elegant and ecient method for the calculation of forces on Cartesian boundaries that realizes one signic ant step to FSI simulations.

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