Lattice Boltzmann Method for Fluid-Structure Interaction with incompressible NeoHookean materials in small perturbations

Abstract

This paper deals with the numerical modelling of the interaction between a fluid and an incompressible solid (Neo Hookean) in small perturbations with the lattice Boltzmann method (LBM). In order to use a monolithic formulation and to solve the whole problem with the lattice Boltzmann method, an Eulerian approach is employed for the solid medium. The initial problem is thus transformed into a diphasic problem and a unique LBM solver is used for both phases (fluid and solid). With this approach, the force at the fluid-solid interface does not need to be explicitly computed. It is intrinsic to the method. This new method approach is validated with three academic cases: the deformation of a solid at the bottom of a lid driven cavity, with steady and unsteady boundary conditions at the top wall of the cavity and the deformation and motion of a disk in a lid driven cavity.

Results are false. A few mistakes have been found since the submission