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An explicit model for three-dimensional fluid-structure interaction using LBM and $$p$$-FEM. (English) Zbl 1213.76148
Bungartz, Hans-Joachim (ed.) et al., Fluid-structure interaction II. Modelling, simulation, optimization. Selected papers based on the presentations at the first international workshop on computational engineering – special topic fluid-structure interactions, Herrsching, Germany, October 2009. Berlin: Springer (ISBN 978-3-642-14205-5/hbk; 978-3-642-14206-2/ebook). Lecture Notes in Computational Science and Engineering 73, 285-325 (2010).
The authors present an explicit coupling model for bi-directional fluid-structure interaction problems with very large structural displacements, where the fluid is modeled via the lattice Boltzmann method (LBM) coupled with a high-order finite element discretization of the structure. The results of the M. Krafczyk postdoctical thesis, given in the article [M. Krafczyk, J. Tolke, E. Rank and M. Schulz, Comput. Struct. 79, 2031–2037 (2001)] are used. After the presentation of LBM followed by a description of the necessary transformation of physical quantities into the lattice Boltzmann system, the authors give a brief description of the $$p$$-version of finite element method applied to structural dynamics. Then the coupling approach is described and boundary conditions are formulated. The validation of the methodology is given via comparison with experimental data. The methodology is extended to three dimensions and applied to a sphere falling in cylinder. The methodology is also applied to a three-dimensional plate in a cross-flow; this example exhibits geometrically nonlinear deformations induced by the fluid. The results are verified by comparing them to numerical and semi-analytic solutions. Additionally, the results are compared with results obtained by the commercial ALE-finite volume-$$h$$-FEM fluid-structure interaction solver Ansys Multiphysics. The comparisons demonstrate the applicability of the proposed methodology to problems of (arbitrarily) large deformations and of large scale.
For the entire collection see [Zbl 1201.76008].

##### MSC:
 76M28 Particle methods and lattice-gas methods 76M10 Finite element methods applied to problems in fluid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
##### Keywords:
falling sphere; plate; geometrically nonlinear deformation
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