Coupled finite element–lattice Boltzmann analysis

A coupled finite element (FE) and lattice Boltzmann (LB) numerical scheme to model the deformation of a porous solid through which fluid flows could offer an attractive solution strategy. As a precursor to a complete simulator, we review the two methodologies and show an initial proof of concept for a coupling method solving one- and multi-dimensional diffusion problems. The accuracy and computational efficiency of the combined method is presented and compared for simple problems that offer analytical solutions. The effects of changing temporal discretisations and diffusivities at the FE–LB interface, as well as iterating towards convergence, are described. The results demonstrate for the first time a transfer of state variables across the FE–LB interface for this class of problems.