A Fluid–Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-Conforming Interfaces
We consider a fluid–structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two radial basis function (RBF) inter-grid operators, one Π fs from master to slave, and the other Π sf from slave to master. Then, we enforce the kinematic condition by equating the fluid velocity at the interface as the image through Π fs of the temporal derivative of the structural displacement. On the other hand, the dynamic interface condition is fulfilled via a variational method where the strong form of the structural normal stress is obtained as the image through Π sf of the strong form of the fluid normal stress. A numerical verification is carried out for a straight cylinder and for a patient-specific arterial bypass geometry. This new method is easy to implement and optimally accurate.
The research of D. Forti was supported by the Swiss National Foundation (SNF), project No. 140184. The research of S. Deparis and A. Quarteroni was partly supported by the PASC project “Integrative HPC Framework for Coupled Cardiac Simulations”. We acknowledge Prof. P. Gervasio for the fruitful discussions and suggestions. We gratefully acknowledge the Swiss National Supercomputing Centre (CSCS) for providing us the CPU resources under project ID s475. We also thank the LifeV community.
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