标题： 二维中囊泡悬浮液的低分辨率模拟 显示英文标题

标题： Low-resolution simulations of vesicle suspensions in 2D

摘要： 囊泡悬浮液出现在许多生物和工业应用中。 这些悬浮液由于与主体流体的相互作用，以及其大变形和非线性弹性特性，表现出丰富的和复杂的囊泡动力学。 许多现有的最先进的数值方案可以解析这种复杂的囊泡流动。 然而，即使使用可证明最优的算法，这些模拟在计算上仍然可能很昂贵，特别是对于含有大量囊泡的悬浮液。 在本文中，我们研究了多种算法经验修正方法的影响，试图使低分辨率模拟更加稳定和更具预测性。 基于对多种流动配置的经验研究，我们提出了一种尝试以系统方式整合这些修正的方法。 这种低分辨率方案是我们之前工作 Quaife 和 Biros (2014) 以及 Quaife 和 Biros (2016) 的扩展。 我们的低分辨率校正算法（LRCA）包括防混叠和膜重新参数化，以避免囊泡膜中的虚假振荡，自适应时间步长和排斥力以处理囊泡碰撞，并对囊泡面积和弧长进行校正，以保持物理上的囊泡形状。 我们通过将低分辨率模拟与高保真、完全解析的对应物进行比较，进行了系统的误差分析。 我们观察到， LRCA 使得囊泡悬浮液的高效且统计准确的低分辨率模拟成为可能，同时它能快 10 倍到 100 倍。 显示英文摘要

摘要： Vesicle suspensions appear in many biological and industrial applications. These suspensions are characterized by rich and complex dynamics of vesicles due to their interaction with the bulk fluid, and their large deformations and nonlinear elastic properties. Many existing state-of-the-art numerical schemes can resolve such complex vesicle flows. However, even when using provably optimal algorithms, these simulations can be computationally expensive, especially for suspensions with a large number of vesicles. In this paper, we investigate the effect of a number of algorithmic empirical fixes in an attempt to make low-resolution simulations more stable and more predictive. Based on our empirical studies for a number of flow configurations, we propose a scheme that attempts to integrate these fixes in a systematic way. This low-resolution scheme is an extension of our previous work Quaife and Biros (2014) and Quaife and Biros (2016). Our low-resolution correction algorithms (LRCA) include anti-aliasing and membrane reparametrization for avoiding spurious oscillations in vesicles' membranes, adaptive time stepping and a repulsion force for handling vesicle collisions and, correction of vesicles' area and arc-length for maintaining physical vesicle shapes. We perform a systematic error analysis by comparing the low-resolution simulations of dilute and dense suspensions with their high-fidelity, fully resolved, counterparts. We observe that the LRCA enables both efficient and statistically accurate low-resolution simulations of vesicle suspensions, while it can be 10x to 100x faster.