Impulse Models for Fluid Motion with Flexible Boundaries

Cortez 9816951研究人员开发了新的数值方法，用于解决涉及柔性边界和不可压缩流体相互作用的问题。 这些问题的典型应用在生物学和生理学中被发现。 所采用的方法包括基于脉冲变量的拉格朗日和欧拉方法，这些方法结合了来自其他数值技术（如涡流和投影方法）的联合收割机元素。 发展了一种适用于高雷诺数流动的混合粒子方法。 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解释。 粘性效应是用确定性方法模拟的，该方法是用涡流单极子进行涡量扩散的。 本文还发展了一种求解中等雷诺数流动中这些问题的基于网格的隐式差分方法。 利用拉格朗日表示的灵活的边界，研究者和他的合作者使用拉格朗日脉冲方法的想法来描述网格解决方案的框架内的浸入边界的演变。 研究人员强调了对现有数值方法的改进，以解决这类问题。具有薄柔性移动边界的流体流动问题的数值解的部分动机是生物学和生理学中广泛的潜在应用。 例如，内耳的膜、心脏或肺的壁、肌肉组织、游泳的水母和鳗鱼可以被建模为嵌入流体中的薄膜。 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完全理解。 可靠的数值模拟的发展和可用性，可以帮助我们了解这种常见的自然现象是非常重要的。 数值方法可用于对新的心脏瓣膜设计进行改进的计算机模拟;可以研究内部有流体的可折叠管的计算机模拟，例如因疾病而变弱的动脉;可以分析单个生物体游泳运动的效率以及动物群体的明显同步模式;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。 此类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交叉点。

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.