CAREER: Regularization methods for fluid/filament interactions in three dimensions

研究人员开发、分析和应用了嵌入不可压缩流体中的弹性丝运动的计算技术。这种一般情况发生在许多物理环境中，包括微生物的运动、水生动物的游泳、弹性体周围的流体流动、气泡运动等等。该项目包括开发与大范围长度尺度相对应的流动的数值方法。这些方法是基于沿细丝使用的力场，这些细丝由局部但光滑的项组成，而不是增量分布。然后，导出了由力引起的流体速度和细丝速度的正则表达式，作为方法的基础。这种方法的重要特点是，它消除了力假定为三角形分布时通常存在的奇异性，弹性边界内的流体体积守恒得非常好，并且可以达到高精度。这项工作的目的是将众所周知的数值技术扩展到沿细丝的力驱动的三维流动，并扩展到整个长度尺度。对这些方法进行了分析，以建立和改进它们的稳定性、收敛和精度性质。所追求的应用包括各种各样的鞭毛运动，围绕障碍物的柔性膜的运动，以及其他。微生物在液体中的运动和血液在毛细血管中的流动是可以用计算方法研究的两个现象。能够准确模拟这类运动的计算机技术非常有价值，因为它们可以用来确定动脉如何阻塞，鞭毛生物如何在人体内执行特定功能，以及这种机制中缺陷的影响。从数学的角度来看，这些计算机模拟还没有准备好供科学家使用；有必要提高求解基本方程的精度，并增加方法的可靠性。该项目旨在开发流体与弹性结构相互作用的计算方法。目标是开发高精度的方法，改进它们的数学特性，并将它们应用于生物科学中的问题。

Cortez0094179 The investigator develops, analyzes, and appliescomputational techniques for the motion of elastic filamentsembedded in an incompressible fluid. This general situationarises in many physical contexts, including the motion ofmicroorganisms, swimming of aquatic animals, fluid flow aroundelastic bodies, bubble motion and more. The project encompassesthe development of numerical methods for flows corresponding to awide range of length scales. The methods are based on the use ofa force field along filaments made of localized but smooth termsrather than delta distributions. Regular expressions for thefluid and filament velocities induced by the forces are thenderived as the basis for the methods. Important properties ofthis approach are that it eliminates the singularities that wouldnormally be present if the forces are assumed to be deltadistributions, the volume of fluid within elastic boundaries isconserved extremely well, and high accuracy can be achieved. Thework is aimed at extending well-known numerical techniques tothree-dimensional flows driven by forces along filaments and tothe full range of length scales. Analysis of the methods iscarried out to establish and improve their stability, convergenceand accuracy properties. The applications that are pursuedinclude a wide variety of flagellar motions, the motion offlexible membranes around obstacles, and others. The motion of microorganisms in a liquid and the flow ofblood in capillaries are two examples of phenomena that can bestudied with computational methods. Computer techniques that canaccurately simulate motions of this type are very valuablebecause they can be used to determine how arteries becomeobstructed or how flagellated organisms perform specificfunctions in the human body and the effects of defects in thismechanism. From a mathematical point of view, these computersimulations are not ready for scientists to use; there is a needto improve the accuracy with which the underlying equations arebeing solved and increase the reliability of the methods. Thisproject is aimed at developing computational methods for fluidflows interacting with elastic structures. The goal is to develophigh-accuracy methods, improve on their mathematical properties,and apply them to problems from biological sciences.