胶体悬浮液模拟的脉动力耦合法
Fluctuating force-coupling method for simulations of colloidal suspensions
摘要：
微颗粒悬浮液模拟中的布朗运动的分辨率对于再现单个颗粒的正确动力学以及提供悬浮液性质的准确表征是至关重要的。然而，在模拟中包括这些效应可能是计算密集型的，这是由于需要在每个时间步长处确定与配置相关的随机位移。在本文中，我们引入波动力耦合方法（FCM），以克服这个困难，提供了一个快速的方法来模拟胶体悬浮液在大规模。我们明确地表明，通过迫使周围的流体与波动的应力和采用FCM框架来获得粒子的运动，得到随机粒子的速度和角速度，满足波动耗散定理。即使在FCM近似中包含高阶多极（例如应力片）时，该结果也成立。通过几个数值实验，我们证实了我们的分析结果，并证明了波动FCM的有效性，也显示了如何布朗漂移可以解决采用适当的时间积分方案和共轭梯度法。
英文摘要：
The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including these effects in simulations, however, can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step. In this paper, we introduce the fluctuating force-coupling method (FCM) to overcome this difficulty, providing a fast approach to simulate colloidal suspensions at large-scale. We show explicitly that by forcing the surrounding fluid with a fluctuating stress and employing the FCM framework to obtain the motion of the particles, one obtains the random particle velocities and angular velocities that satisfy the fluctuation-dissipation theorem. This result holds even when higher-order multipoles, such as stresslets, are included in the FCM approximation. Through several numerical experiments, we confirm our analytical results and demonstrate the effectiveness of fluctuating FCM, showing also how Brownian drift can be resolved by employing the appropriate time integration scheme and conjugate gradient method.
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