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年的《美国回收与再投资法》（公法111-5）资助的。生物流体结构相互作用动态的数值建模是数学生物学的迅速扩展的研究领域。我们将考虑两种成功计算流体结构相互作用的策略，这些策略在应用数学社区中很流行：正规化Stokeslet的方法（在Stokes制度中适当）和沉浸的边界方法（当惯性力不容忽视时）。这两种方法都在部分流行，因为它们为建模与不可压缩流体相互作用的复杂边界提供了相当简单的选择。不幸的是，在这两种情况下，都有大量的计算瓶颈，严重限制了这些方法在各种问题上的效率和/或准确性。例如，在这两种方法中，结构的刚度都可以按数量级限制计算的允许的明确时步。此外，对生物结构的精细规模特征进行建模的愿望需要在空间自适应计算和并行处理。尽管尚未尝试过这些算法的分析和实施，但多分辨率的时间整合方法和基于快速求和的基于积分的方法的进步提供了实质上提高这些方法的准确性和效率的技术。我们的目标是完成为流体结构问题实施有效的平行，适应性，多分辨率的时间整合和快速求和方法所必需的数学和计算分析，并建立计算基础架构，并促进生物学科学中的研究人员，以在大规模的平行计算中进行质量良好的计算机和计算机的计算范围内的计算机构图。科学家要在生物学和医学领域的广泛问题中获得更详细的了解，例如鱼游泳或昆虫的飞行，通过形状或质地的变化来减少植物和树木的阻力，以及心脏中的血液或消化系统，肾脏，肾脏以及肺部的材料流中的血液或材料流动。特别是，我们的软件将允许研究人员开始研究日益复杂的问题，例如流体流过毛茸茸的附属物，或多种结构或生物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，工程师将生物学寻求设计策略。例如，对水母中鱼类或喷气推进的鳍变形的了解对生物界和从事微水下车辆的工程师都很感兴趣。 我们的计算方法可以应用于模拟生物植物中其他感兴趣的系统，包括肌肉氢化体，例如章鱼臂，earth虫子和大象躯干。