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

TL;DR

This paper introduces a monolithic lattice Boltzmann method for fluid-structure interaction involving incompressible Neo-Hookean solids under small perturbations, enabling unified simulation without explicit interface force calculations.

Contribution

It develops a novel Eulerian-based monolithic LBM approach for fluid-structure interaction with Neo-Hookean materials, simplifying interface force computation.

Findings

Successfully validated with academic test cases

Accurately captured solid deformation and motion

Demonstrated method's stability and effectiveness

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.