An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions
An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions
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一种在稠密斯托克斯悬浮液数值模拟中包含润滑力的精确方法
DOI：
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发表时间：
2015
影响因子：
3.7
通讯作者：
T. Nguyen
中科院分区：
文献类型：
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作者：
A. Lefebvre;Benoît Merlet;T. Nguyen
我们解决了计算在斯托克斯流中以给定旋转和平移速度移动的 $N$ 固体球形颗粒之间的流体动力和扭矩的问题。我们考虑原始的流体-粒子模型，而不引入新的假设或模型。我们的方法包括当一些颗粒彼此靠近时可能发生的奇异润滑相互作用。主要的新功能是短程相互作用传播到整个流动，包括准确的多体润滑相互作用。该方法建立在预先存在的流体求解器的基础上，并且对于该求解器的选择是灵活的。该误差是流体求解器在计算非奇异流（即可忽略的短程相互作用）时产生的误差。因此，只需要少量的自由度，我们就能在合理的计算成本内获得非常准确的模拟。我们的方法与 Sangani & Mo 提出的方法密切相关（Phys. Fluids，第 6 卷，1994 年，第 1653-1662 页），但与后者相反，它不需要参数调整。我们将我们的方法与 Durlofsky 等人的斯托克斯动力学进行比较。 （J. Fluid Mech.，第 180 卷，1987 年，第 21-49 页）并表明前者具有更高的精度（通过分析和数值实验）。
We address the problem of computing the hydrodynamic forces and torques among $N$ solid spherical particles moving with given rotational and translational velocities in Stokes flow. We consider the original fluid–particle model without introducing new hypotheses or models. Our method includes the singular lubrication interactions which may occur when some particles come close to one another. The main new feature is that short-range interactions are propagated to the whole flow, including accurately the many-body lubrication interactions. The method builds on a pre-existing fluid solver and is flexible with respect to the choice of this solver. The error is the error generated by the fluid solver when computing non-singular flows (i.e. with negligible short-range interactions). Therefore, only a small number of degrees of freedom are required and we obtain very accurate simulations within a reasonable computational cost. Our method is closely related to a method proposed by Sangani & Mo (Phys. Fluids, vol. 6, 1994, pp. 1653–1662) but, in contrast with the latter, it does not require parameter tuning. We compare our method with the Stokesian dynamics of Durlofsky et al. (J. Fluid Mech., vol. 180, 1987, pp. 21–49) and show the higher accuracy of the former (both by analysis and by numerical experiments).