晶格Boltzmann方法中流体力的计算  

Hydrodynamic force evaluation in lattice Boltzmann method

作　　者：闻炳海[1,2] 张超英[2] 方海平[1] 

机构地区：[1]中国科学院上海应用物理研究所水科学与技术研究室,上海201800 [2]广西师范大学广西多源信息挖掘与安全重点实验室,桂林541004

出　　处：《中国科学：物理学、力学、天文学》2017年第7期165-186,共22页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:11290164;11162002;11362003;11462003);中国科学院知识创新工程领域前沿项目(编号:KJZD-EW-M03);广西自然科学基金(编号:2014GXNSFAA118018);广西高校科学技术研究重点项目(编号:KY2015ZD017)资助

摘　　要：晶格Boltzmann方法是起源于动理学理论和元胞自动机的介观数值模拟方法,在模拟复杂流体运动,特别是颗粒悬浮运动和多相流等领域取得了显著的成功.在计算流体与结构之间的相互作用力时,通过引入相对速度,提出了伽利略不变的动量交换法.该方法简单、精确、高效,而且与边界的几何形状无关;它只使用局部数据,方便实施并行计算和三维模拟;它具有良好的稳定性,流体力计算结果的波动非常小,甚至不需要进行时间平滑处理.在数值模拟多相流的研究中,基于热力学自由能理论计算非理想力,提出了同时满足热力学一致性和伽利略不变性的多相流模型.该模型物理清晰、易于实施,可以方便地配合不同的状态方程用于模拟各种多相流系统.化学势是驱动相分离和表达润湿性的有效途径,在进一步的研究中,借助化学势计算非理想力,提出了基于化学势的多相流模型.它在数学上等价于基于压力张量计算非理想力的模型,但是避免了计算压力张量和张量散度,获得了更高的计算效率.该模型配合化学势边界条件,可以有效地模拟润湿现象,其接触角可以通过表面化学势进行线性调节.The lattice Boltzmann method is a mesoscopic numerical method originating from kinetic theory and the cellular automaton concept. It has been successfully used to simulate complex flows, especially particle suspensions and multiphase flows. In this paper, we review our recent work on fluid-structure interactions and nonideal force evaluations. We introduced the relative velocity into the treatment of fluid-structure interfacial dynamics and proposed a Galilean invariant momentum exchange method. The method is simple, accurate and efficient. It is independent of boundary geometries and only uses the local data, thus it is convenient to implement parallelization and 3D simulations. The numerical simulations are so vastly improved that the force fluctuations are very small and a time average procedure becomes unnecessary. To simulate phase separation and two-phase flow, we directly evaluated the nonideal force based on the free energy and proposed a multiphase flow model. Thermodynamic consistency and Galilean invariance of the model are theoretically satisfied and numerically verified. This model can be easily implemented and cooperated with various equations of state to simulate all kinds of the multiphase systems. Chemical potential is an effective way to drive phase transition or express surface wettability. In the further study, we proposed another multiphase flow model based on chemical potential. It is mathematically equivalent to the previous one, but is more computationally efficient owing to avoiding the calculations of pressure tensor and tensor divergence. Together with the chemical potential boundary condition, the model can effectively simulate wetting phenomena. The numerical results show that the contact angle can be linearly tuned by the surface chemical potential.

关 键 词：晶格Boltzmann方法 流固相互作用 非理想力 多相流 润湿性 

分 类 号：O35[理学—流体力学]