On lattice Boltzmann method for solving fluid-structure interaction problems

Abstract

This work presents computational modeling aspects for studying Fluid-Structure Interaction (FSI). The Lattice Boltzmann Method (LBM) is employed to solve the fluid mechanics considering the incompressible Navier-Stokes equations. The flows studied are complex due to the presence of arbitrary shaped obstacles. The obstacles alters the bulk flow adding complexity to the analysis. In this work the Euler-Lagrange equations are obtained employing the Principle of Virtual Power Balance (PVPB). Consequently, the functional dependencies between the mechanical state and every kinematic compatible loadings are established employing variational arguments. This modeling technique allows to study the fluid-solid boundary constraint. In this context the fluid-solid interface is handled employing the Immersed Boundary Method (IBM). The IBM deals with the fluid-solid interface equilibrium equations performing an interpolation of forces between Lagrangian nodes (solid domain) and Eulerian Lattice grid (fluid domain). In this work a different version of this methodology is studied that allows to obtain more accurate solutions. To show the capabilities of the implemented LBM-IBM solver several experiments are done showing the agreement with the benchmarks results available in literature.