Modeling the flow of dense suspensions of deformable particles in three dimensions
Modeling the flow of dense suspensions of deformable particles in three dimensions
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DOI：
10.1103/physreve.75.066707
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发表时间：
2007-06-01
影响因子：
2.4
通讯作者：
Munn, Lance L.
中科院分区：
文献类型：
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作者：
Dupin, Michael M.;Halliday, Ian;Munn, Lance L.
我们在这里描述了一个严格和准确的模型，用于模拟三维可变形粒子（DPs）。该方法是非常通用的，很容易模拟各种类型的可变形粒子，如囊泡、胶囊和生物细胞。每个DP都被明确地分解并在周围的牛顿流体中平流。DPs具有首选的静止形状（例如，囊泡为球形，红细胞为双凹形）。该模型使用了一个经典的混合系统：欧拉方法用于纳维-斯托克斯求解器（晶格玻尔兹曼方法），拉格朗日方法用于DP网格的演化。耦合是通过晶格玻尔兹曼速度场完成的，该速度场将力传递到DPs的膜上。这种方法的新颖之处在于它能够（通过设计）在当前计算限制的范围内模拟大量的DPs：我们简单而有效的方法是：(i)使用晶格玻尔兹曼方法，因为它在低雷诺数下公认的效率和易于并行化；（ii）使用粗网格（大约500个节点）和弹簧模型来约束（必要时）局部面积、总面积、单元体积、局部曲率和局部主应力。通过一系列的定量比较，我们表明这种方法与更常见的膜电位函数方法（但在数值上昂贵）相当。为了证明该模型的能力，我们模拟了200个密集排列的红细胞的流动——这是一项具有计算挑战性的任务。模型是非常有效的,需要的分钟中的单个DP 50亩mx40μmx40μm模拟域和几小时在80亩200 DPs mx30μmx30μm。此外,模型是高度可伸缩的和有效的与其他模型相比流动的血液细胞,使它理想的和独特的工具研究微血管的血液循环或囊泡或胶囊流(或不同的粒子的混合物)。除了直接预测任何几何形状的复杂悬浮液中的流体动力学外，该模型还允许确定精确的经验规则，这可能会改进现有的宏观连续体模型。
We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common-yet numerically expensive-approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells-a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 mu mx40 mu mx40 mu m simulation domain and only hours for 200 DPs in 80 mu mx30 mu mx30 mu m. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.