FRG - Advanced Algorithms and Software for Problems in Computational Bio-Fluid Dynamics

FRG - 用于计算生物流体动力学问题的先进算法和软件

• 批准号: 0854961
• 负责人: Laura Miller
• 金额: --
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0854961&HistoricalAwards=false
• 关键词: FRG; Advanced; Algorithms; Software; Problems

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The numerical modeling of the dynamics of biological fluid-structure interactions is a rapidly expanding research area in mathematical biology. We will consider two successful strategies for computing fluid-structure interactions which are popular in the applied mathematics community: the Method of Regularized Stokeslets (appropriate in the Stokes regime), and the Immersed Boundary Method (when inertial forces cannot be ignored). Both of these methods are popular partially because they offer a reasonably straightforward option for modeling complex boundaries interacting with an incompressible fluid. Unfortunately, in both cases there are substantial computational bottlenecks which severely limit the efficiency and/or accuracy of these methods for a wide class of problems. For example, in both methods, the stiffness of the structure can restrict the allowable explicit time-step of a computation by orders of magnitude. In addition, the desire to model fine scale features of biological structures requires spatially adaptive computations and parallel processing. Recent advances in multi-resolution temporal integration methods and integral based methods for fast summation and elliptic equations provide the technology to substantially increase the accuracy and efficiency of these methods, although the analysis and implementation of these algorithms has not been attempted. Our goal is to complete the mathematical and computational analysis necessary to implement efficient parallel, adaptive, multi-resolution time integration and fast summation methods for fluid-structure problems and to build a computational infrastructure that will enable researchers in the biological sciences to perform numerical simulations of biological systems on massively parallel computers.The development of improved algorithms and a computational interface to facilitate massively parallel computation will enable scientists to obtain a much more detailed understanding of the fluid dynamics in a wide range of problems in the biological and medical fields such as the swimming of fish or flying of insects, the reduction of drag in plants and trees by changes in shape or texture, and the pumping of blood in the heart or the flow of materials in the digestive system, the kidney, and the lungs. In particular, our software will allow researchers to begin to study increasingly complex problems such as fluid flow through bristled appendages, or interactions or coordination between multiple structures or organisms. Beyond obtaining fundamental insight into biological design, this work could motivate innovation in the field of biomimetics, where engineers look to biology for design strategies. For example, improved understanding of fin deformations in fish or jet propulsion in jellyfish is of interest to both the biological community and engineers working on micro underwater vehicles. Our computational methods can be applied to model other systems of interest in biommetics including muscular hydrostats such as octopus arms, earthworm bodies, and elephant trunks.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。生物流固相互作用动力学的数值模拟是数学生物学中一个迅速发展的研究领域。我们将考虑在应用数学界流行的两种计算流固相互作用的成功策略：正则化stokeslet方法（适用于Stokes状态）和浸入边界法（当惯性力不能忽略时）。这两种方法都很受欢迎，部分原因是它们为与不可压缩流体相互作用的复杂边界建模提供了一种相当直接的选择。不幸的是，在这两种情况下，都存在大量的计算瓶颈，这些瓶颈严重限制了这些方法对大量问题的效率和/或准确性。例如，在这两种方法中，结构的刚度可以在数量级上限制计算的允许显式时间步长。此外，对生物结构精细尺度特征的建模需要空间自适应计算和并行处理。快速求和和椭圆方程的多分辨率时间积分方法和基于积分的方法的最新进展为大大提高这些方法的精度和效率提供了技术，尽管这些算法的分析和实现尚未尝试。我们的目标是完成必要的数学和计算分析，以实现有效的并行，自适应，多分辨率时间积分和快速求和方法的流体结构问题，并建立一个计算基础设施，使生物科学研究人员能够在大规模并行计算机上进行生物系统的数值模拟。改进的算法和计算界面的发展促进大规模并行计算将使科学家能够获得更详细了解广泛的流体动力学问题在生物和医学领域如鱼的游泳或飞行的昆虫、植物和树木的减少阻力的变化形状或纹理,和血液在心脏的泵或流动的材料在消化系统,肾脏,还有肺。特别是，我们的软件将允许研究人员开始研究越来越复杂的问题，如流体流过刚毛附体，或多个结构或生物体之间的相互作用或协调。除了获得对生物设计的基本见解之外，这项工作还可以激发仿生学领域的创新，工程师们在仿生学领域寻找设计策略。例如，提高对鱼的鳍变形或水母的喷气推进的理解是生物界和研究微型水下航行器的工程师都感兴趣的。我们的计算方法可以应用于模拟其他生物仿生学中感兴趣的系统，包括肌肉流体静力学，如章鱼臂、蚯蚓体和象鼻。