Analysis of open boundary effects in unsteady lattice Boltzmann simulations

The effects of the interaction between the open boundaries (inflow and outflow) and the fluid domain are studied in unsteady lattice Boltzmann (LB) simulations of fluid flow. The confined unsteady laminar flow past a square cylinder is used as test case due to the continuous vortex shedding generated in the wake of the cylinder. Three different approaches to treat open boundaries are considered as they are expected to be representative of the most common ones typically used in LB. We conclude that lattice Boltzmann methods suffer from the same problems with open boundaries as other compressible or pseudo-compressible approximations for the numerical solution of fluid flows: these boundaries reflect pressure waves and these have a relevant influence on the solution and convergence rate of both steady and unsteady flows, even at very low Reynolds numbers. However, practical solutions considering zero derivatives at the outflow or non-reflecting boundaries are possible.