Towards the simulations of inertial dense particulate flows with a volume-averaged lattice Boltzmann method

In this paper, we first introduce a novel lattice Boltzmann method (LBM) for the VANS equations which relies on an adaptation of the streaming step, while requiring no additional forcing terms. Second, we combine the method with an advection-diffusion LBM to obtain a simple multiphase model, which forms a first step towards an Euler-Euler model for dense particulate flows. It takes the phases' volume fractions and simple drag forces into consideration but neglects some inter-particle and hydrodynamic forces as well as turbulence. The LBM's convergence to the VANS equations is investigated in four test cases with analytical solutions, two of which contain spatially or temporally fluctuating particle concentrations. The combined multiphase model is validated using a Rayleigh-Taylor instability test case.