Consistent lattice Boltzmann methods for the volume averaged Navier-Stokes equations

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. & COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

We propose a new lattice Boltzmann scheme that approximates the volume averaged Navier-Stokes equations using a pressure correction forcing term. The scheme takes into account spatially and temporally varying local volume fractions, and a Chapman-Enskog analysis proves its consistency towards the VANSE limit up to higher order terms. Numerical validation shows the second order convergence of velocity and pressure, making this lattice Boltzmann method the first to correctly recover the pressure with second order for space-time varying volume fractions.