Improvement of the Stokesian Dynamics method for systems with a finite number of particles
Improvement of the Stokesian Dynamics method for systems with a finite number of particles
复制标题
有限粒子系统斯托克斯动力学方法的改进
DOI：
10.1017/s0022112001006735
复制
发表时间：
2002
影响因子：
3.7
通讯作者：
K. Ichiki
中科院分区：
文献类型：
--
作者：
K. Ichiki
对多粒子系统的Stokesian动力学方法进行了改进。采用了水动力相互作用的直接计算，而不是强加周期性边界条件。两大困难涉及计算的准确性和速度。在这项工作中讨论的精度与润滑校正无关，而是侧重于多极膨胀，到目前为止，它只被表述为所谓的FTS版本或一阶力矩。通过在粒子中心计算力矩和速度矩的实空间多极展开系统地改进了这一点，其中速度矩通过速度导数计算；速度导数的引入使公式及其扩展变得简单明了。矩化约为不可约形式是通过笛卡尔不可约张量实现的。这种化简对于形成一个定义良好的线性方程组作为广义迁移问题是必不可少的。截断的阶数在原则上不受限制，两体问题的显式计算显示的阶数最高可达7。采用共轭梯度迭代法，在每次迭代中以广义迁移率矩阵与力矩的点积作为试验值，提高了计算速度。这提供了一个O（N2）方案，其中N是系统中的粒子数。采用快速多极子法进一步改进了每次迭代中广义迁移性问题的计算，得到了非自适应版本的O(N)格式。研究了N = 40万个粒子系统的实际问题。对于迁移性问题，迭代次数不变，可实现O(N)性能；然而，对于电阻问题，迭代次数几乎增加到N1/2，精度高达10−6，总成本似乎为0 （n2 /2）。
An improvement of the Stokesian Dynamics method for many-particle systems is presented. A direct calculation of the hydrodynamic interaction is used rather than imposing periodic boundary conditions. The two major difficulties concern the accuracy and the speed of calculations. The accuracy discussed in this work is not concerned with the lubrication correction but, rather, focuses on the multipole expansion which until now has only been formulated up to the so-called FTS version or the first order of force moments. This is improved systematically by a real-space multipole expansion with force moments and velocity moments evaluated at the centre of the particles, where the velocity moments are calculated through the velocity derivatives; the introduction of the velocity derivatives makes the formulation and its extensions straightforward. The reduction of the moments into irreducible form is achieved by the Cartesian irreducible tensor. The reduction is essential to form a well-defined linear set of equations as a generalized mobility problem. The order of truncation is not limited in principle, and explicit calculations of two-body problems are shown with order up to 7. The calculating speed is improved by a conjugate-gradient-type iterative method which consists of a dot-product between the generalized mobility matrix and the force moments as a trial value in each iteration. This provides an O(N2) scheme where N is the number of particles in the system. Further improvement is achieved by the fast multipole method for the calculation of the generalized mobility problem in each iteration, and an O(N) scheme for the non-adaptive version is obtained. Real problems are studied on systems with N = 400 000 particles. For mobility problems the number of iterations is constant and an O(N) performance is achieved; however for resistance problems the number of iterations increases as almost N1/2 with a high accuracy of 10−6 and the total cost seems to be O(N3/2).