Algorithms for Simulating Flows with Elastic Components

模拟弹性组件流动的算法

• 批准号: 0511309
• 负责人: Noel Walkington
• 金额: $ 19.73万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0511309&HistoricalAwards=false
• 关键词: Algorithms; Simulating; Flows; Elastic; Components

This project considers the construction and analysis of algorithms tosimulate fluid systems containing elastic components. Polymers, suchas liquid crystals, are an important class of such fluids, and in thisinstance the elastic properties of the molecules are usuallyincorporated into a continuum model. Another example is blood flowwhere the elasticity of the red blood cells gives rise tonon-Newtonian behavior. This problem was motivated by collaborativework with engineers who wish to determine the distribution of anddamage to red blood cells in the small clearances within mechanicalheart assist devices. Since these clearances are of comparabledimension to the cells, it is necessary to explicitly model the cellsat the micrometer scale in order to determine their distribution andthe stresses they experience. The mathematical structure of theequations modeling viscoelastic polymers and blood are very similar,and insight gained in one of them sheds light on the other.The ability to simulate the flow of complex materials on a computer isa key technology required for the design and development of many "nextgeneration" products, such as micro-mechanical devices, bio-materials,and prosthetic organs. For example, a major mode of failure inmechanical heart assist devices is the formation of clots (thrombosis)which are primarily initiated by damage to the red blood cells. Thisphenomena is difficult to control and the ability to simulate it on acomputer it would represent a breakthrough which would eliminate muchof the expensive and time consuming experimentation currentlyrequired. The equations used to model such phenomena are complex andpoorly understood, and much of the research proposed herein is directedto revealing the theoretical (mathematical) properties of thesemodels. This work complements the more practical approaches undertakenin the engineering community and at the national laboratories.

该项目考虑了模拟包含弹性部件的流体系统的算法的构建和分析。聚合物（例如液晶）是此类流体的重要类别，在这种情况下，分子的弹性特性通常被纳入连续介质模型中。另一个例子是血流，其中红细胞的弹性产生非牛顿行为。这个问题是由与工程师合作提出的，他们希望确定机械心脏辅助装置内小间隙中红细胞的分布和损伤。由于这些间隙与细胞的尺寸相当，因此有必要在微米尺度上对细胞进行显式建模，以确定它们的分布和它们承受的应力。模拟粘弹性聚合物和血液的方程的数学结构非常相似，在其中一个方程中获得的见解可以为另一个方程提供启发。在计算机上模拟复杂材料流动的能力是许多设计和开发所需的关键技术。 “下一代”产品，如微型机械装置、生物材料和假肢器官。例如，机械心脏辅助装置的主要故障模式是形成凝块（血栓形成），这主要是由红细胞损伤引起的。这种现象很难控制，而在计算机上模拟它的能力将代表着一项突破，它将消除目前所需的许多昂贵且耗时的实验。用于模拟此类现象的方程非常复杂且难以理解，本文提出的大部分研究旨在揭示这些模型的理论（数学）属性。这项工作补充了工程界和国家实验室采取的更实用的方法。