Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast

Abstract

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio

“…The continuum DI approach can easily apply high-order upwind schemes to get more accurate and stable solutions, which are especially useful for the stable discretization of convective terms in the N-S and C-H equations. As compared with the continuum DI approach, the LBE method [9,15,[17][18][19][20][21] has been developed into an alternative powerful tool. Many effective LB models have been successfully developed, such as the thermodynamically consistent model of Swift et al.…”

Chemical-potential-based lattice Boltzmann method for nonideal fluids

“…Inamuro et al used an asymptotic analysis to accommodate the lack of Galilean invariance and extended the model to simulate multiphase flows with large density ratio [18,19]. Zheng et al correctly recovered the Cahn-Hilliard equation to capture the phase interface and Shao et al further considered the effect of local density variation in the momentum equation [20,21].…”

Pore-scale simulation of effects of coal wettability on bubble-water flow in coal cleats using lattice Boltzmann method

“…However, this model is proved to be restricted to densitymatched binary fluids (Fakhari and Rahimian, 2010). Recently, a modified new model considering the local density variation is developed by Shao et al (2014).…”

“…In this paper, the LB model developed by Shao et al (2014) and the partial wetting boundary condition (Briant, 2002) are applied to simulate bubble-water flow in coal cleats at pore-scale. The influences of coal wettability and capillary pressure on gas-water two-phase flow behaviours in a coal cleat are investigated.…”