论文标题
在一类自由化多相晶格Boltzmann模型中实现热力学一致性
Achieving thermodynamic consistency in a class of free-energy multiphase lattice Boltzmann models
论文作者
论文摘要
自由能晶格Boltzmann（LB）模型是LB社区中的主要多相模型之一。本研究集中在一类自由能LB模型上，其中通过强迫术语将热力压力张量的差异或由化学势表达的等效形式纳入LB方程中。尽管这类自由能LB模型在连续水平上可能在热力学上是一致的，但由于数值误差，它在离散晶格水平下具有热力学不一致[Guo等，物理评论E 83，036707（2011）]。数值错误项主要包括两个部分，一个来自离散的梯度操作员，另一个可以在高阶Chapman-Enskog分析中识别。在本文中，我们提出了一种改进的方案，以消除上述自由能LB模型的热力学不一致。改进的方案是通过修改标准LB方程式的方程来构建的，通过该方程，$ \ nabla \ left的离散化（{{ρc_ {\ rm {s}}}}^{\ rm {\ rm {2}}}}}} \ right）$不再涉及力量和数量的误差。随后进行数值模拟以验证提出的方案。数值结果表明，改进的方案能够消除热力学不一致，并且与基于标准强迫的自由能LB模型相比，可以显着减少伪电流。
The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Physical Review E 83, 036707 (2011)]. The numerical error term mainly includes two parts, one comes from the discrete gradient operator and the other can be identified in a high-order Chapman-Enskog analysis. In this paper, we propose an improved scheme to eliminate the thermodynamic inconsistency of the aforementioned class of free-energy LB models. The improved scheme is constructed by modifying the equation of state of the standard LB equation, through which the discretization of $\nabla \left( {ρc_{\rm{s}}^{\rm{2}}} \right)$ is no longer involved in the force calculation and then the numerical errors can be significantly reduced. Numerical simulations are subsequently performed to validate the proposed scheme. The numerical results show that the improved scheme is capable of eliminating the thermodynamic inconsistency and can significantly reduce the spurious currents in comparison with the standard forcing-based free-energy LB model.
