Impulse Models for Fluid Motion with Flexible Boundaries

Cortez9816951研究人员开发了新的数值方法来解决涉及柔性边界及其浸入的不可压缩流体相互作用的问题。这类问题在生物学和生理学中都有典型的应用。所采用的方法包括基于脉冲变量的拉格朗日方法和欧拉方法，它们结合了涡旋和投影法等其他数值技术的元素。提出了一种适用于高雷诺数流动的混合质点方法。在这种情况下，浸没边界力的累积效应通过脉冲变量的演变来考虑。粘性效应用涡单极子涡量扩散的确定性方法来模拟。本文还发展了基于有限差分网格的方法来求解中等雷诺数流动中的这些问题。利用柔性边界的拉格朗日表示，研究人员和他的合作者使用拉格朗日冲量方法的思想来描述网格解框架内浸没边界的演化。研究人员强调了对这类问题现有数值方法的改进。具有薄而灵活移动边界的流体流动问题的数值解部分是由于在生物学和生理学中广泛的潜在应用。例如，内耳、心壁或肺壁、肌肉组织、游泳的水母和鳗鱼的膜可以被模拟为嵌入液体中的薄膜。这些例子是日常生活的一部分，但它们的许多技术方面还没有被完全理解。开发和提供可靠的数值模拟，帮助我们理解这种常见的自然现象是非常重要的。数值方法可以用来对新的心脏瓣膜设计进行改进的计算机模拟；可以研究内部有液体的可折叠管道的计算机模拟，例如因疾病而变弱的动脉；可以分析单个生物游泳运动的效率以及动物群体明显同步的模式；可以设计新的推进机制。例如，波动运动存在于各种大小的生物体中，因为它是精子以及鳗鱼和蛇的首选游泳模式。这些问题的数学解决方案位于自然科学、数学建模和科学计算的十字路口。

Cortez9816951The investigator develops new numerical methods for the solution of problems involving the interaction of flexible boundaries and the incompressible fluids in which they are immersed. Typical applications of such problems are found in biology and physiology. The approaches pursued include Lagrangian and Eulerian methods based on impulse variables, which combine elements from other numerical techniques such as vortex and projection methods. A hybrid particle method is developed for high Reynolds number flows. In this case the accumulated effect of immersed boundary forces is accounted for through the evolution of impulse variables. The viscous effects are modeled using a deterministic method for the diffusion of vorticity using vortex monopoles. Finite-difference grid-based methods are also developed for the solution of the these problems in moderate Reynolds number flows. Making use of the Lagrangian representation of the flexible boundaries, the investigator and his collaborators use ideas from the Lagrangian impulse method to describe the evolution of the immersed boundaries within the framework of the grid solution. The researchers highlight improvements to existing numerical methods for this type of problems.The numerical solution of fluid flow problems with thin flexible moving boundaries is motivated partly by the wide range of potential applications in biology and physiology. For example, the membranes of the inner ear, the walls of the heart or lungs, muscle tissue, swimming jellyfish and eels can be modeled as thin membranes embedded in a fluid. These examples are part of everyday life and yet many of their technical aspects are not fully understood. The development and availability of reliable numerical simulations that could help our understanding of such commonly occurring natural phenomena is of great importance. Numerical methods can be used to conduct improved computer simulations of new heart valve designs; computer simulations of collapsible tubes with a fluid inside, such as arteries weakened by disease, can be studied; efficiency in swimming motions of a single organism as well as the apparently synchronized patterns of groups of animals can be analyzed; new propulsion mechanisms can be devised. Undulatory motion, for example, is present in organisms of a wide range of sizes because it is the preferred swimming mode of spermatozoa as well as eels and snakes. The mathematical solution of such problems lies at the crossroads of natural sciences, mathematical modeling and scientific computing.