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

Cortez 0094179 研究者发展、分析和应用计算技术来研究嵌入在不可压缩流体中的弹性体的运动。 这种普遍情况出现在许多物理环境中，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。 该项目评估了与各种长度尺度相对应的流动数值方法的发展。 该方法是基于使用ofa力场沿着丝由本地化，但顺利termsrather不是三角洲分布。 然后推导出由力引起的流体和细丝速度的正则表达式，作为方法的基础。 这种方法的重要特性是，它消除了奇异性，通常会出现，如果力被假定为δ分布，弹性边界内的流体体积是非常好的保存，并可以实现高精度。 这项工作的目的是扩展众所周知的数值技术，以三维流驱动力沿着长丝和到的长度尺度的全部范围。 对这些方法进行了分析，以建立和改进它们的稳定性、收敛性和精度特性。 所追求的应用包括各种各样的鞭毛运动，障碍物周围的柔性膜的运动，以及其他。 液体中微生物的运动和毛细血管中血液的流动是可以用计算方法研究的现象的两个例子。 能够精确模拟这种运动的计算机技术是非常有价值的，因为它们可以用来确定动脉是如何阻塞的，或者有鞭毛的生物体是如何在人体内执行特定功能的，以及这种机制的缺陷的影响。 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;有必要提高基本方程求解的准确性，并增加方法的可靠性。 本项目旨在发展流体与弹性结构相互作用的计算方法。 其目标是开发高精度的方法，改善其数学性质，并将其应用于生物科学的问题。

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.