A decoupled and stabilized lattice Boltzmann method for multiphase flow with large density ratio at high Reynolds and Weber numbers

Abstract

A decoupled lattice Boltzmann method (LBM) with improved numerical stability is developed from the conventional multiple relaxation time (MRT) model by eliminating the second-order mutual effects of viscosity modes. The dependency between relaxation times and viscosity is decoupled to remove the O(u3) errors in the original model, and thus a stabilization strategy is proposed by adjusting relaxation times without changing the local viscosity under the mass and momentum conservations. This new model still stays in the conventional MRT framework and keeps the advantages of simplicity and efficiency of LBM implementation. The decoupled MRT is demonstrated to be valid for high-speed flow with Galilean invariance. Moreover, the pseudopotential model is employed in this paper to present the improvement of numerical stability in simulating the large-density-ratio multiphase flows at high Reynolds (Re) and Weber (We) numbers. Droplet collision is achieved at density ratio 1153, Re = 34474 and We = 28212. Droplet splashing is achieved at density ratio 6637, Re = 34474 (and 71928) and We = 30538 (and 259). Droplet impacting on dry wall is achieved at density ratio 5720, Re = 11462 (and 22982) and We = 13573 (and 166). All collision regimes are simulated by the decoupled MRT from low Re (We) to high Re (We).