New numerical techniques for non-Newtonian flow simulations and their application to modelling of complex flows

调查者的研究是对非牛顿流体流动的流体动力学进行及时的研究。研究人员将系统地研究高效计算模型包的设计和开发，该模型包可以处理复杂流体的各种宏观模型，也可以处理传统数值方法难以捉摸的广泛的物理参数。除了一般的算法开发，包括像多重网格法这样的快速求解方法，研究人员的目标是研究和理解实验流变学领域中出现的各种新物理现象的适当数学模型。与牛顿流体或聚合物流体不同，蠕虫状胶束流体中的落球在下落时会经历持续的振荡。该项目的这一部分将涉及测试与蠕虫状胶束流体相关的各种宏观模型，并将导致为落球实验识别正确的数学模型。这位研究人员还将为所谓的高魏森伯格数问题建立数学基础。尽管最近取得了重大进展，但对于包括著名的Oldroyd-B模型在内的一大类非牛顿流体模型，成功的计算仍然局限于非常有限的Weissenberg数。研究人员将实现计算机模拟高弹性流体流动的新方法，即具有高魏森伯格数的模型，以模拟和理解另一种新观察到的有趣的物理现象--弹性湍流。由大分子组成的流体，称为非牛顿流体或复杂流体，可以产生许多新的物理现象。非牛顿流体的例子在我们的日常生活中随处可见，包括熔融的塑料、含有聚合物添加剂的发动机油、油漆以及许多生物流体，如蛋清和血液。设计、实现和使用数值方法对这种物理现象进行计算机模拟需要充分掌握非牛顿流体，研究人员的研究结果有望在工业上有重要的应用。同样，聚合物工程师可以进行详细的计算机辅助设计(CAD)研究，其中将至少定性地建立原材料的分子结构和产品的最终性质之间的联系。生产问题将被预测，并通过改进设计部分解决。人们还可以考虑使用在线计算流变学模型与适当的控制算法相结合，以提供基于物理的智能过程控制技术。研究人员的研究结果可以创造更多的机会。

The research of the investigator is on the timely study of thefluid dynamics of non-Newtonian fluid flows. The investigatorwill examine systematically the design and development of an efficientcomputational modelling package that can handle variousmacroscopic models of complex fluids and also a wide spectrum ofphysical parameters that have been elusive for conventionalnumerical methods. In addition to general algorithmic developmentsincluding the fast solution method like the multigrid methods, theinvestigator aims to study and understand proper mathematicalmodels for a great variety of new physical phenomena arising inthe area of experimental rheology. In particular, the investigatorwill tackle an important challenge of modelling a continualoscillation of falling sphere in worm-like micellar fluid flows.In contrast to the Newtonian fluid or the polymeric fluids, thefalling sphere in a worm-like micellar fluid undergoes a continualand sustained oscillation as it falls. This part of the projectwill involve testing various macroscopic models that are relevant forthe worm-like micellar fluids and will lead to identification of the rightmathematical models for a falling sphere experiment. Theinvestigator will also address a mathematical foundation forthe so-called high Weissenberg number problem. Despite recentsignificant progress, the successful computations are stillconfined to very restrictive size of the Weissenberg number for alarge class of non-Newtonian fluid models including the well-knownOldroyd-B model. The investigator will implement the new numericalmethods for the computer simulations of highly elastic fluidflows, namely, models with high Weissenberg number to simulate andunderstand another newly observed intriguing physical phenomenon,the elastic turbulence.Fluids comprised of large macromolecules, known as non-Newtonianfluids or complex fluids, can generate many new physicalphenomenon. Examples of non-Newtonian fluids can be foundthroughout our daily lives, including molten plastics,engine oils with polymeric additives, paints, and many biologicalfluids such as egg white and blood. The design, implementation,and the use of numerical methods for the computer simulation ofsuch physical phenomena requires full grasp of non-Newtonianfluids and the results of the investigator's research areexpected to have significant applications, for example in industry.Namely, a polymer engineer could perform elaborateComputer Aided Design (CAD) studies in which the link between themolecular architecture of the raw material and the finalproperties of the product would be established, at leastqualitatively. Production problems would be predicted andpartially overcome through improved design. One could also thinkof using an on-line computational rheology model in concert withappropriate control algorithms to provide for intelligent,physics-based process control techniques. There are many moreopportunities that the investigator's research resultscould generate.