Shao J Y, Shu C, Huang H B, Chew Y T
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore.
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):033309. doi: 10.1103/PhysRevE.89.033309. Epub 2014 Mar 19.
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.
本文提出了一种基于自由能的相场格子玻尔兹曼方法来模拟具有密度差的多相流。本方法旨在改进郑-舒-周（ZSC）模型[Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)]，以便在动量方程中正确考虑密度差。原始的ZSC模型在格子玻尔兹曼方程（LBE）中使用粒子分布函数来表示平均密度和动量，这无法在动量方程中正确考虑局部密度变化的影响。为了正确考虑这一点，LBE中的粒子分布函数必须针对局部密度和动量。然而，求解这种分布函数的LBE时会遇到严重的数值不稳定性。为了克服这一困难，本文引入了一种类似于李-林（LL）模型[Lee and Lin, J. Comput. Phys. 206, 16 (2005)]中使用的变换，将针对局部密度和动量的粒子分布函数转换为针对平均密度和动量的粒子分布函数。结果，本模型仍然使用针对平均密度和动量的粒子分布函数，同时将LBE中局部密度变化的影响作为一个强迫项来考虑。数值算例表明，本模型和LL模型都能正确模拟具有密度差的多相流，并且本模型在求解精度方面比ZSC模型有明显改进。在计算时间方面，本模型比ZSC模型效率低，但比LL模型效率高得多。
