A fast Chebyshev method for the Bingham closure with application to active nematic suspensions
A fast Chebyshev method for the Bingham closure with application to active nematic suspensions
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DOI：
10.1016/j.jcp.2021.110937
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Scott Weady;David B. Stein;M. Shelley
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文献类型：
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作者：
Scott Weady;David B. Stein;M. Shelley
连续介质动力学理论为颗粒悬浮体系的分析和模拟提供了重要的工具。当这些粒子是各向异性时，在动力学描述中加入粒子取向矢量会产生一个2 d− 1维的理论，这变得难以模拟，特别是在三维或粒子高度排列的近状态下。仅跟踪粒子分布函数的矩的粗粒度理论提供了更有效的模拟框架，但需要闭合假设。对于非极性粒子的特殊情况，宾汉封闭被发现与基本的动力学理论吻合得很好;然而封闭的计算是不平凡的，需要在每个时间步长的每个空间离散点求解一个经常接近奇异的非线性方程。在本文中，我们提出了一个强大的，准确的，高效的数值计算方案，用于评估宾汉封闭，具有可控的误差/效率权衡。为了证明该方法的实用性，我们进行了高分辨率模拟的粗粒度连续模型的悬浮液中的活性粒子的参数制度无法访问的动力学理论。对这些模拟的分析表明，不准确地计算闭包可以有效地限制粗粒度字段中的空间分辨率。将这些模拟推到我们的方法所能实现的高空间分辨率，揭示了悬浮指向矢场中涡度和拓扑缺陷之间的耦合，以及这种主动流体模型中尺度之间能量传递的特征。
Continuum kinetic theories provide an important tool for the analysis and simulation of particle suspensions. When those particles are anisotropic, the addition of a particle orientation vector to the kinetic description yields a 2 d− 1 dimensional theory which becomes intractable to simulate, especially in three dimensions or near states where the particles are highly aligned. Coarse-grained theories that track only moments of the particle distribution functions provide a more efficient simulation framework, but require closure assumptions. For the particular case where the particles are apolar, the Bingham closure has been found to agree well with the underlying kinetic theory; yet the closure is non-trivial to compute, requiring the solution of an often nearly-singular nonlinear equation at every spatial discretization point at every timestep. In this paper, we present a robust, accurate, and efficient numerical scheme for evaluating the Bingham closure, with a controllable error/efficiency tradeoff. To demonstrate the utility of the method, we carry out high-resolution simulations of a coarse-grained continuum model for a suspension of active particles in parameter regimes inaccessible to kinetic theories. Analysis of these simulations reveals that inaccurately computing the closure can act to effectively limit spatial resolution in the coarse-grained fields. Pushing these simulations to the high spatial resolutions enabled by our method reveals a coupling between vorticity and topological defects in the suspension director field, as well as signatures of energy transfer between scales in this active fluid model.