Consistent multiple-relaxation-time lattice Boltzmann method for the volume-averaged Navier-Stokes equations

The volume-averaged Navier-Stokes equations (VANSE), serving as the cornerstone of various fluid-solid multiphase models, have recently been reported to be solved using a pressure-based lattice Boltzmann (LB) method that decouples the pressure from density and exhibits good numerical performance [1]. However, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, this paper introduces a multiple-relaxation-time LB method, which incorporates a provisional equation of state into the redefined equilibrium distribution to decouple the void fraction from density, and readjusts a correction force to produce correct pressure term. Also, Galilean invariance of the recovered VANSE is guaranteed by devising a source term in moment space, effectively eliminating unwanted numerical errors in viscous stress tensor. Through Chapman-Enskog analysis and comprehensive numerical validations, this proposed scheme is demonstrated to be capable of recovering consistent VANSE with second-order accuracy, and offers better numerical stability over previous schemes for handling void fraction fields with large gradients and spatiotemporal distributions.