Li Q, Luo K H, Li X J
Energy Technology Research Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016709. doi: 10.1103/PhysRevE.86.016709. Epub 2012 Jul 23.
The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.
伪势格子玻尔兹曼（LB）模型是LB领域中广泛使用的多相模型。在该模型中，通常通过强迫格式实现的相互作用力被用于模拟导致相分离的分子相互作用。因此，强迫格式在伪势LB模型中有望发挥重要作用。在本文中，我们旨在解决伪势LB模型中强迫格式的一些关键问题。首先，将对单陈强迫格式[单和陈，《物理评论E》47，1815（1993）]和精确差分法强迫格式[库佩什托克等，《计算数学及其应用》58，965（2009）]进行理论和数值分析。将展示这两种格式的性质及其恢复的宏观方程。其次，通过理论分析，我们将揭示在伪势LB模型中不同强迫格式表现出不同性能这一现象背后的物理原理。此外，基于该分析，我们将提出一种改进的强迫格式，并通过数值证明该改进格式可被视为在伪势LB模型中实现热力学一致性的一种替代方法。
