Pressure condition for lattice Boltzmann methods on domains with curved boundaries

We propose a lattice Boltzmann algorithm for an average pressure boundary condition at outlets in pipe flow systems. The advantage of this boundary condition is that only the average pressure is used to recover the non-trivial flow fields. The asymptotic analysis shows that this algorithm works for general curved boundaries and renders a second order accurate velocity and a first order accurate pressure approximation of the incompressible Navier–Stokes solution. Here, we verify the accuracy by numerical simulations of a Poiseuille flow and a less symmetric flow with non-trivial pressure field in channels inclined with arbitrary angle, and flows in a pipe with three outlets.