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CAREER: Fast Algorithms for Particulate Flows

职业：颗粒流的快速算法

基本信息

批准号：
1454010
负责人：
Shravan Veerapaneni
金额：
$ 42.07万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-09-15 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1454010&HistoricalAwards=false
关键词：
CAREER Fast Algorithms Particulate Flows

项目摘要

The objective of this Faculty Early Career Development (CAREER) project is to build stable, high-accuracy, and optimal algorithms for direct numerical simulations of particulate flows. Dense suspensions of deformable particles in viscous fluids are ubiquitous in natural and engineering systems. Examples include drop, bubble, vesicle, swimmer, and blood cell suspensions. Unlike simple Newtonian fluids, the laws describing their flow behavior are not well established, owing to the complex interplay between the deformable micro-structure and the macro-scale flow. For instance, interactions between soft particles modify their trajectories and cause shear-induced diffusion, and interaction with confining walls controls the spatial organization of the suspensions. Besides experiments, direct numerical simulations are often the only means for gaining insights into the non-equilibrium behavior of such complex fluids. Hence, there is a need for robust and optimal algorithms that are scalable. Integrated with the research effort, this project will undertake educational, mentoring, and outreach activities including a new interdisciplinary graduate-level course on computational methods for complex fluids and an interactive education module illustrating the non-intuitive phenomena observed in complex fluid systems that is accessible to high school students. The specific aims of this project include (i) highly accurate algorithms to compute the nearly singular integrals that arise within the context of boundary integral methods when particles approach very close to each other when subjected to flow, (ii) fast, high-order, and adaptive algorithms to simulate multiphase flows through arbitrary periodic geometries, and (iii) stable time-marching and reparameterization schemes for the coupled systems of stiff, nonlinear, time-dependent differential and integro-differential equations governing the evolution of particles and some material concentration on their surfaces (e.g., surfactants or multi-phase lipids). The proposed computational infrastructure will lead to better predictive capabilities for blood flow through complex geometries, margination of platelets and targeted carriers, and new design tools for microfluidic devices. They can be applied to a large class of particulate flow problems. Besides fluid mechanics, the proposed numerical methods and the computational infrastructure can be applied to solve partial differential equations that arise in various other disciplines. The research outcomes will have an impact on a broad spectrum of disciplines in sciences and engineering.

这个教师早期职业发展（Career）项目的目标是为颗粒流动的直接数值模拟建立稳定、高精度和最佳的算法。黏性流体中可变形颗粒的密集悬浮物在自然和工程系统中普遍存在。例子包括滴、泡、囊泡、游泳者和血细胞悬浮液。与简单的牛顿流体不同，由于可变形的微观结构与宏观尺度流动之间的复杂相互作用，描述其流动行为的定律尚未很好地建立。例如，软颗粒之间的相互作用改变了它们的轨迹并引起剪切诱导扩散，与围壁的相互作用控制了悬浮液的空间组织。除了实验之外，直接数值模拟往往是了解这种复杂流体的非平衡行为的唯一手段。因此，需要可扩展的鲁棒和最优算法。与研究工作相结合，该项目将承担教育、指导和推广活动，包括一个新的跨学科研究生水平的复杂流体计算方法课程，以及一个交互式教育模块，说明在复杂流体系统中观察到的非直觉现象，该模块面向高中生。该项目的具体目标包括(i)计算边界积分方法中出现的近似奇异积分的高精度算法，当粒子在流动时彼此非常接近时，（ii）快速，高阶和自适应算法来模拟通过任意周期几何的多相流，以及（iii）稳定的时间推进和重新参数化方案，用于刚性，非线性，随时间变化的微分方程和积分微分方程控制粒子的演化及其表面上的一些物质浓度（例如，表面活性剂或多相脂质）。提出的计算基础设施将带来更好的预测能力，通过复杂的几何形状，血小板和靶向载体的边界，以及微流体装置的新设计工具。它们可以应用于大量的颗粒流动问题。除了流体力学之外，所提出的数值方法和计算基础设施也可以应用于求解其他学科中出现的偏微分方程。研究成果将对科学和工程领域的广泛学科产生影响。