粘性剪切流中刚体双周期悬浮运动的积分方程法
An integral equation method for the simulation of doubly-periodic suspensions of rigid bodies in a shearing viscous flow
摘要：
考虑到流变学的应用，我们提出了一个快速求解器的时间依赖性的有效粘度的无限晶格包含一个或多个中性浮力光滑刚性颗粒每单位细胞，在一个二维斯托克斯流体与给定的剪切速率。在每一个时间，流动性问题被重新制定为第二类边界积分方程，然后离散到频谱精度的Nystrom方法和迭代求解，通常给出10位数的精度。它的解决方案控制的演变粒子的位置和角度的一阶系统的常微分方程。制定放置在一个严格的基础上，通过定义一个广义周期格林函数的斜晶格。数值上，周期化的积分算子被分裂成一个近像和|通过快速多极子方法在线性时间内应用|加上通过代理Stokeslets廉价解决的校正字段。我们使用重心求积来准确地评估粒子相互作用和速度场，即使距离比节点间距近得多。使用一阶时间步进，我们模拟，例如，25个椭圆每个单元格3位数的精度在桌面上在1小时每剪切时间。我们的例子表明，在很长的时间，力链，和两种类型的爆破（堵塞）的幂律匹配润滑理论的渐近平衡。
英文摘要：
With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid particles per unit cell, in a two-dimensional Stokes fluid with given shear rate. At each time, the mobility problem is reformulated as a 2nd-kind boundary integral equation, then discretized to spectral accuracy by the Nystrom method and solved iteratively, giving typically 10 digits of accuracy. Its solution controls the evolution of particle locations and angles in a first-order system of ordinary differential equations. The formulation is placed on a rigorous footing by defining a generalized periodic Green's function for the skew lattice. Numerically, the periodized integral operator is split into a near image sum|applied in linear time via the fast multipole method|plus a correction field solved cheaply via proxy Stokeslets. We use barycentric quadratures to evaluate particle interactions and velocity fields accurately, even at distances much closer than the node spacing. Using first-order time-stepping we simulate, eg, 25 ellipses per unit cell to 3-digit accuracy on a desktop in 1 hour per shear time. Our examples show equilibration at long times, force chains, and two types of blow-ups (jamming) whose power laws match lubrication theory asymptotics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
