A Fast Algorithm for Simulating Multiphase Flows Through Periodic Geometries of Arbitrary Shape
A Fast Algorithm for Simulating Multiphase Flows Through Periodic Geometries of Arbitrary Shape
复制标题
模拟任意形状周期性几何形状的多相流的快速算法
DOI：
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发表时间：
2015
影响因子：
3.1
通讯作者：
S. Veerapaneni
中科院分区：
文献类型：
--
作者：
Gary R. Marple;A. Barnett;A. Gillman;S. Veerapaneni
本文提出了一种新的边界积分方程（BIE）方法，用于模拟颗粒和多相流在二维任意光滑周期性通道中的流动。作者考虑了一个特殊的系统-多个囊泡悬浮在一个周期性的通道的任意形状-来描述的数值方法和测试其性能。该方法不像经典的BIE方法那样依赖于周期性的绿色函数，而是将自由空间绿色函数与一个小的辅助基相结合，并将周期性作为一个额外的线性条件。因此，我们可以利用现有的自由空间求解器库，求积和快速算法，并处理大量的囊泡在一个几何复杂的通道。在空间中的光谱精度实现使用周期性梯形规则和产品求积，而一阶半隐式方案演变粒子通过明确地处理囊泡通道相互作用。新的约束校正公式的引入，保持减少的囊泡面积，独立的时间步长的数量。通过使用两种类型的快速算法，（i）的快速多极方法（FMM）的囊泡和囊泡通道的流体动力学相互作用的计算，和（ii）一个快速的直接求解器的BIE上的固定通道的几何形状，计算成本降低到$O（N）$每个时间步长，其中$N$是空间离散化的大小。此外，直接求解器在$t = 0$时反转壁BIE算子，存储其压缩表示并在每个时间步应用它来发展囊泡位置，从而与经典方法相比节省了大量成本。数值实验表明，在笔记本电脑上，每一个时间步可以在不到一分钟的时间内演化出$N=128，000$的模拟。
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple vesicles suspended in a periodic channel of arbitrary shape---to describe the numerical method and test its performance. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with a small auxiliary basis, and imposes periodicity as an extra linear condition. As a result, we can exploit existing free-space solver libraries, quadratures, and fast algorithms, and handle a large number of vesicles in a geometrically complex channel. Spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures, while a first-order semi-implicit scheme evolves particles by treating the vesicle-channel interactions explicitly. New constraint-correction formulas are introduced that preserve reduced areas of vesicles, independent of the number of time steps taken. By using two types of fast algorithms, (i) the fast multipole method (FMM) for the computation of the vesicle-vesicle and the vesicle-channel hydrodynamic interaction, and (ii) a fast direct solver for the BIE on the fixed channel geometry, the computational cost is reduced to $O(N)$ per time step where $N$ is the spatial discretization size. Moreover, the direct solver inverts the wall BIE operator at $t = 0$, stores its compressed representation and applies it at every time step to evolve the vesicle positions, leading to dramatic cost savings compared to classical approaches. Numerical experiments illustrate that a simulation with $N=128, 000$ can be evolved in less than a minute per time step on a laptop.
影响因子：
10.8
作者：
Decuzzi, P.;Godin, B.;Ferrari, M.
通讯作者：
Ferrari, M.