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

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。生物流体-结构相互作用动力学的数值模拟是数学生物学中一个迅速扩大的研究领域。我们将考虑两种在应用数学界流行的计算流固耦合的成功策略：正则化Stokelet方法(适用于Stokes区域)和浸没边界方法(当惯性力不可忽略时)。这两种方法都很受欢迎，部分原因是它们为模拟与不可压缩流体相互作用的复杂边界提供了一个相当简单的选择。不幸的是，在这两种情况下，都存在大量的计算瓶颈，这严重限制了这些方法对于广泛类别问题的效率和/或精度。例如，在这两种方法中，结构的刚度可以限制按数量级进行计算的允许显式时间步长。此外，为了对生物结构的精细尺度特征进行建模，需要进行空间自适应计算和并行处理。多分辨率时间积分方法和用于快速求和和椭圆方程的基于积分的方法的最新进展提供了显著提高这些方法的精度和效率的技术，尽管这些算法的分析和实现尚未被尝试。我们的目标是完成对流体结构问题的高效并行、自适应、多分辨率时间积分和快速求和方法的必要的数学和计算分析，并建立一个计算基础设施，使生物科学的研究人员能够在大规模并行计算机上对生物系统进行数值模拟。改进的算法和促进大规模并行计算的计算接口的开发将使科学家能够更详细地了解生物和医学领域中广泛的流体动力学问题，如鱼的游泳或昆虫的飞行，通过形状或纹理的变化减少植物和树木的阻力，心脏中的血液或消化系统、肾脏和肺中的物质流动。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，如通过毛茸茸的附属物的流体流动，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外，这项工作还可以激励仿生学领域的创新，在仿生学领域，工程师们从生物学中寻找设计策略。例如，更好地了解鱼类的鳍变形或水母的喷气推进，对生物界和从事微型水下航行器工作的工程师都很感兴趣。我们的计算方法可以应用于生物化学中其他感兴趣的系统的建模，包括肌肉止水剂，如章鱼手臂、蚯蚓身体和大象鼻子。

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.