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.

本文主要研究非牛顿流体流动的数值逼近在物理应用中的应用。这种流体流动在我们的日常生活中非常丰富，从我们体内的血液流动到塑料等聚合物材料的生产。有两个原型问题考虑在该项目中：（i）缺陷边界条件的最优控制，和（ii）非牛顿流体中的弹性介质。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在分裂算子的同时实现最佳收敛速率的求解算法。此外，由于大量的未知数近似，有必要开发有效的解决这些问题。所提出的研究解决解耦方案，其稳定性和收敛性的问题。该研究的主要贡献是发展了耦合系统中非牛顿流动的鲁棒数值格式，以及非牛顿流动最优控制的分析和数值研究。对涉及牛顿流动的多学科问题进行了广泛的研究，但迄今为止，数学和数值研究非牛顿流动还很落后。 由于许多重要的生物和工程过程涉及非牛顿流体流动，在这些应用中有很大的数学支持的需求。 该研究拓宽了物理环境下非牛顿流体流动问题数值模拟的数学基础。此外，该研究通过为重要过程的数值模拟提供改进的算法，使生物医学和聚合物工业受益。