An Explicit Model for Three-Dimensional Fluid-Structure Interaction using LBM and p-FEM

An explicit coupling model for the simulation of surface coupled fluid-structure interactions with large structural deflections is introduced. Specifically, the fluid modeled via the Lattice Boltzmann Method (LBM) is coupled to a high-order Finite Element discretization of the structure. The forces and velocities are discretely computed, exchanged and applied at the interface. The low compressibility of the Lattice Boltzmann Method allows for an explicit coupling algorithm. The proposed explicit coupling model turnes out to be accurate, very efficient and stable even for nearly incompressible flows. It was implemented in three software components: VirtualFluids (fluid), AdhoC (structure) and FSIsce (a communication library). The validity of the approach is demonstrated in two dimensions by means of comparing numerical results to measurements of an experiment. This experiment involves a flag-like structure submerged in the laminar flow field of an incompressible fluid where the structure exhibits large, geometrically non-linear, self excited, periodic motions. The methodology is then extended to three dimensions. Its performance is first demonstrated via the computation of a falling sphere in a pipe. The close correspondence of the results obtained by application of the numerical scheme compared to a semi-analytic solution is demonstrated. The proposed explicit coupling model is then extended to a plate in a cross flow. We verify the results by comparing them to results obtained by application of the commercial ALE-Finite Volume—h-FEM Fluid-Structure interaction solver Ansys Multiphysics. Additional examples demonstrate the applicability of the proposed methodology to problems of (arbitrarily) large deformations and of large scale.