A filtered cumulant lattice Boltzmann method for violent two-phase flows

Abstract

The Lattice Boltzmann Method (LBM) has been successfully applied to simulate various two-phase flow problems such as Rayleigh-Taylor instability, rising bubble, and droplet dynamics. However, the method, known as two-phase LBM, faces difficulty in simulating violent two-phase flow problems such as dam-breaking and liquid jet breakup where the density ratio and Reynolds number are high, and there are rapid and complex topological changes. In this paper, we address the problem by using a filtered cumulant LBM. The incompressible two-phase flow equations are solved by using a velocity-based formulation of two-phase LBM with a cumulant collision model to stably simulate problems with high density ratio and Reynolds number. There is no pressure iteration in this formulation and we can keep the simplicity of the cumulant model. To further enhance the stability in violent flows, a second order filter is applied on the velocity field which can be turned off for non-violent flows. For interface capturing, a conservative phase-field LBM which guarantees the mass conservation is employed. The proposed method is first validated using five non-violent flow problems and the results are in good agreements with experimental and computational references. The proposed method is then employed to solve three violent flow problems and the results are in qualitatively good agreements with experimental and computational references. The proposed method is more diffusive than the unfiltered model but is stable for all problems simulated in this paper. These results can be used as a preliminary study on violent two-phase flow simulation using two-phase LBM.