Numerical Approximations of Non-Newtonian Fluid Flows with Applications

非牛顿流体流动的数值近似及其应用

• 批准号: 1016182
• 负责人: Hyesuk Lee
• 金额: $ 20.99万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016182&HistoricalAwards=false
• 关键词: Numerical; Approximations; Non; Newtonian; Fluid

This research is focused on numerical approximation of non-Newtonian fluid flows in physical applications. Such fluid flows are abundant in our everyday lives, from the flow of blood in our bodies to the production of polymeric material such as plastics. There are two prototypal problems considered in the project: (i) optimal control for defective boundary conditions, and (ii) non-Newtonian flow within an elastic medium. Blood flow is one of most important examples related to such situations as a non-Newtonian flow interacts with an elastic vessel wall, where only flow rate or mean pressure is specified on each inflow and outflow boundary. The model problems in this research involve either coupled domains representing multi-physics behavior or coupled state-adjoint systems. This increases the numerical complexity as both stress and velocity must be resolved in the domains, and the strong interaction between the governing equations requires solution algorithms that achieve optimal convergence rates while splitting the operators. Additionally, because of the large number of unknowns to be approximated, there is a need to develop efficient solvers for these problems. The proposed research addresses issues on decoupling schemes, and their stability and convergence. The primary contribution of the research is the development of robust numerical schemes for non-Newtonian flows in coupled systems, and analytical and numerical study of optimal control for non-Newtonian flows.There have been extensive studies on multidisciplinary problems involving Newtonian flows, but to date mathematical and numerical investigations of non-Newtonian flows are still far behind. Because of the many important biological and engineering processes involving non-Newtonian fluid flow, there is a great demand for mathematical support in these applications. The proposed research broadens the mathematical basis for the numerical simulation of non-Newtonian fluid flow problems in physical settings. Also the research benefits biomedical and polymer industries by providing improved algorithms for the numerical simulation of important processes.

这项研究的重点是物理应用中非牛顿流体流动的数值近似。从我们体内的血液流动到塑料等聚合材料的生产，这种流体流动在我们的日常生活中随处可见。该项目考虑了两个原型问题：（i）有缺陷边界条件的最优控制，以及（ii）弹性介质内的非牛顿流动。血流是与非牛顿流与弹性血管壁相互作用的情况相关的最重要的示例之一，其中在每个流入和流出边界上仅指定流速或平均压力。本研究中的模型问题涉及表示多物理行为的耦合域或耦合状态伴随系统。这增加了数值复杂性，因为应力和速度都必须在域中求解，并且控制方程之间的强相互作用需要求解算法在分解算子的同时实现最佳收敛速度。此外，由于有大量的未知数需要近似，因此需要为这些问题开发有效的求解器。拟议的研究解决了解耦方案及其稳定性和收敛性问题。该研究的主要贡献是开发了耦合系统中非牛顿流的鲁棒数值方案，以及非牛顿流最优控制的分析和数值研究。涉及牛顿流的多学科问题已经有了广泛的研究，但迄今为止，对非牛顿流的数学和数值研究仍然远远落后。 由于许多重要的生物和工程过程涉及非牛顿流体流动，因此这些应用中对数学支持的需求很大。 所提出的研究拓宽了物理环境中非牛顿流体流动问题数值模拟的数学基础。此外，该研究还为重要过程的数值模拟提供了改进的算法，从而使生物医学和聚合物行业受益。