A lattice Boltzmann based reference map technique for fluid–structure interaction

The lattice Boltzmann (LB) method is a widely-used simulation approach for fluids that uses a mesoscopic probabilistic view of particle motion to reassemble macroscopic fluid quantities. The LB method uses a fixed Eulerian grid, and is particularly effective for simulating fluid flows in complex geometries. Here we present an extension to the LB method to model fluid–structure interaction problems involving solids undergoing large deformation. We use the reference map technique to model the large solid deformation on the same fixed Eulerian grid used in LB, thereby providing a unified discretization scheme that greatly simplifies the coupling between the two phases. Examples of incompressible neo-Hookean solids immersed within a quasi-incompressible Navier–Stokes fluid show this method is flexible and robust in handling a range of fluid–structure interactions. The method is a favorable candidate for simulations of soft colloidal mixtures, eroding sediments, or interacting microswimmers.