  We derive a novel lattice Boltzmann scheme, which uses a pressure correction
forcing term for approximating the volume averaged Navier-Stokes equations
(VANSE) in up to three dimensions. With a new definition of the zeroth moment
of the Lattice Boltzmann equation, spatially and temporally varying local
volume fractions are taken into account. A Chapman-Enskog analysis, respecting
the variations in local volume, formally proves the consistency towards the
VANSE limit up to higher order terms. The numerical validation of the scheme
via steady state and non-stationary examples approves the second order
convergence with respect to velocity and pressure. The here proposed lattice
Boltzmann method is the first to correctly recover the pressure with second
order for space-time varying volume fractions.
