Pressure boundary condition for the lattice Boltzmann method

We propose a lattice Boltzmann realization for the hydrodynamic pressure drop condition introduced in [J. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations, Int. J. Numer. Methods Fluids 22 (1996) 325–352]. This condition has the advantage that only the average pressure needs to be prescribed at the boundary. In general, a second order accurate velocity and a first order accurate pressure are recovered with the proposed lattice Boltzmann implementation. The analytical investigation is supported by numerical simulations of a Poiseuille flow and a less symmetric flow with nontrivial pressure field.