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

研究者的研究是对非牛顿流体流动的流体动力学的及时研究。该演示文稿将系统地研究设计和开发一个高效的计算建模包，可以处理各种复杂流体的宏观模型，也是一个广泛的物理参数，一直难以捉摸的传统数值方法。除了一般算法的发展，包括快速解决方案的方法，如多重网格方法，研究者的目的是研究和理解适当的物理模型，为各种新的物理现象出现在实验流变学领域。与牛顿流体或聚合物流体不同，蠕虫状胶束流体中的下落球体在福尔斯过程中会经历一个持续的振荡过程。项目的这一部分涉及测试各种与蠕虫状胶束流体相关的宏观模型，并将导致为落球实验确定正确的数学模型。调查人员还将解决所谓的高韦森伯格数问题的数学基础。尽管最近取得了重大进展，成功的计算仍然局限于非常有限的大小的Weissenberg数的一个大类的非牛顿流体模型，包括著名的Oldroyd-B模型。研究人员将采用新的数值方法对高弹性流体流动进行计算机模拟，即高Weissenberg数模型，以模拟和理解另一个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。非牛顿流体的例子可以在我们的日常生活中找到，包括熔融塑料，含有聚合物添加剂的机油，油漆和许多生物流体，如鸡蛋白色和血液。设计，实施和使用数值方法的计算机模拟ofsuch物理现象，需要充分掌握非牛顿流体和研究人员的研究成果预计将有重大的应用，例如在工业中。即，一个聚合物工程师可以进行精细的计算机辅助设计（CAD）在这些研究中，原料的分子结构和产品的最终性质之间的联系将被建立起来，至少是定性的。通过改进设计，可以预测并部分克服生产问题.人们也可以考虑使用在线计算流变学模型与适当的控制算法，以提供智能的，基于物理的过程控制技术。研究者的研究成果可以产生更多的机会。

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.