A scalable computational platform for particulate Stokes suspensions
A scalable computational platform for particulate Stokes suspensions
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DOI：
10.1016/j.jcp.2020.109524
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Wen Yan;Eduardo Corona;D. Malhotra;S. Veerapaneni;M. Shelley
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作者：
Wen Yan;Eduardo Corona;D. Malhotra;S. Veerapaneni;M. Shelley
我们描述了在牛顿斯托克斯流中模拟刚性颗粒悬浮的计算框架。其中一个核心模块是碰撞分辨率算法，该算法克服了粒子碰撞产生的数值限制。该算法扩展了非光滑多体动力学的互补法，用于求解密集刚体悬架中的碰撞问题。该方法将碰撞解决问题表述为在每个时间步上施加几何“不重叠”约束的线性互补问题。然后将其重新表述为一个有约束的二次规划问题，并采用Barzilai-Borwein投影梯度下降法求解。该框架被设计为适用于任何凸粒子形状，例如球体和球柱体，并适用于任何Stokes迁移求解器，包括Rotne-Prager-Yamakawa近似，Stokesian动力学和PDE求解器（例如，边界积分和浸入边界方法）。特别是，这种方法利用牛顿第三定律，记录了整个接触网络。此外，我们描述了一种针对球形颗粒的快速、平行、光谱精确的边界积分方法，能够解决润滑效应。我们在1792个核上显示了弱和强平行缩放到8× 10 4粒子，自由度约为4× 10 7。我们用几个例子证明了这个框架的多功能性，包括粒子团的沉降，以及由驱动旋转的粒子群组成的活性物质系统。
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric ‘non-overlapping’constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, eg, spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (eg, boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8× 10 4 particles with approximately 4× 10 7 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.