A mass-conserved multiphase lattice Boltzmann method based on high-order difference*

Abstract

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew (ZSC), J. Comput. Phys. 218, 353 (2006)] is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out, including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Improved contact angle measurement in multiphase lattice Boltzmann

“…The surface wettability is adjusted by chemical potential, which is an essential parameter coupled to the density gradient. We further used the five-point central difference method [33,35] with fourth order accuracy to calculate the gradients, which involves 5 lattice nodes,…”