An Efficient Algorithm for Hydrodynamical Interaction of Many Deformable Drops
An Efficient Algorithm for Hydrodynamical Interaction of Many Deformable Drops
复制标题
多种可变形液滴流体动力学相互作用的有效算法
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Robert H. Davis
中科院分区：
文献类型：
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作者：
A. Z. Zinchenko;Robert H. Davis
提出了一种高效、精确的三维算法，用于零雷诺数下具有强流体动力相互作用的多个可变形液滴的动力学模拟。液滴与介质的粘度比？，和Bond数是任意的，液滴受重力作用，具有三重周期边界条件。该算法，在每一步，是一个混合的边界积分和经济的多极技术，广泛使用旋转变换和经济截断多极展开，以优化近场相互作用。该代码的一个重要部分是新的“最佳抛物面样条”技术，用于计算跌落表面的法向量和曲率，这大大提高了长时间模拟的质量。实例表明，在一个浓缩的沉降乳状液中，0.25和1，这导致平均沉降速度随时间增加。一个高效率的方法被证明，两个数量级的增益超过标准O（N2 N2？）N~（102）液滴在周期池中的边界积分方法每个液滴103个三角形边界元，因此典型的长时间动态模拟可以在几天或几周内在标准工作站上进行（与使用标准边界积分技术进行相同模拟所需的几年相比）。滴三角剖分和截断的多极展开动力学模拟的影响进行了评估。
An efficient and accurate 3D algorithm for dynamical simulations of many deformable drops with strong hydrodynamical interactions at zero Reynolds numbers is developed. The drop-to-medium viscosity ratio, ?, and the Bond number are arbitrary, and the drops are subject to gravity with stationary triply periodic boundary conditions. The algorithm, at each step, is a hybrid of boundary-integral and economical multipole techniques, with extensive use of rotational transformations and economical truncation of multipole expansions to optimize near-field interactions. A significant part of the code is the new, “best paraboloid-spline” technique for calculating the normal vectors and curvatures on drop surfaces, which greatly improves the quality of long-time simulations. Examples show the phenomenon of clustering in a concentrated sedimenting emulsion for ?=0.25 and 1, which leads to an increase in the average sedimentation velocity with time. A high efficiency of the method is demonstrated, with two orders-of-magnitude gains over the standard O(N2N2?) boundary-integral technique for N~102 drops in a periodic cell with N?~103 triangular boundary elements per drop, so that typical long-time dynamical simulations can be performed in a few days or weeks on a standard workstation (as compared to the several years which would be required for the same simulations using standard boundary-integral techniques). The effects of drop triangulation and truncation of multipole expansions on dynamical simulations are assessed.