Computational Rheology
Computational Rheology
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DOI：
10.1515/arh-2002-0032
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发表时间：
2002
期刊：
影响因子：
1.8
通讯作者：
M. Dressler
中科院分区：
文献类型：
--
作者：
M. Dressler
《计算流变学》是继Crochet、Davis和Walters在1984年出版的《非牛顿流动的数值模拟》一书以及自20世纪80年代中期以来发表的大量综述文章之后，第一本完全致力于该领域的教科书。由于在过去的20年里做了很多工作，计算流变学自那以后经历了巨大的进步，人们对这本新书的期望很高。这本新书的目的是对粘弹性流体的物理模型和理论流变学中有关计算方面的主要挑战进行处理。根据作者的说法，这本书是为应用数学和工程领域的研究人员和学生写的。这本书的第一部分包括第一章到第七章，它给出了几个问题的介绍，这些问题是解决计算非牛顿流体力学问题之前的基本问题。本书的这一部分涉及粘弹性流动方程的推导，应力本构模型的构造，偏微分方程组的数学理论，以及求解粘弹性流动方程的离散化技术和数值算法的基本要素。这本书的第一部分被写得尽可能自成体系。在第一章中，向读者介绍了麦克斯韦模型、开尔文模型，以及非牛顿液体在剪切和单轴拉伸流动中的行为。再者，这位先生。1探讨了高Weissenberg数问题的一些原因，这是计算流变学中的一个关键问题，以及如何设计创新技术来解决/绕过它。第二章主要由两部分组成：首先给出了几个运动量的定义，导出了流体力学中的一些基本结果，然后介绍了应力张量的本构关系。读者感兴趣的是更深入地研究粘弹性的数学，描述粘弹性的实验研究，即。流变学和聚合物液体的微观结构模型(参见。也是第一章。11)可参考其他教科书。接下来的一章。3讨论了基本粘弹性流动方程的数学性质：流动方程解的存在唯一性、边界条件的规范以及在流动区域的某些位置(如拐角或边缘)存在奇性。下一章。4解决了为附加应力张量选择合适的本构方程以使计算机模拟与实验观测的粘弹性液体的性质相一致的困难。此外，还讨论了粘弹性流体的基本材料函数表征和唯象参数进入流动方程的问题。第一章。5和6分别涉及粘弹性流动方程的离散化和离散化方程的数值解。第一章。6介绍了各种不同的求解方法，如有限差分法、伽辽金有限元方法、有限体积法和规范应用流变学第12卷/第6卷qxd 10.01.2003 13：58 Uhr Seite 280
"Computational Rheology" is the first text book dedicated entirely to the field after the 1984 book "Numerical Simulation of Non-Newtonian Flow" by Crochet, Davis, and Walters and numerous review articles which have been published since the mid 1980s. Since much work has been done during the past 20 years and computational rheology has experienced enormous progress since then, the expectations in a new book are high. The objective of this new book is to give a treatment of the physical modeling of viscoelastic fluids and of the main challenges concerning computational aspects in theoretical rheology. According to the authors the book is written for researchers and students in applied mathematics and engineering. The first part of the book comprises chapters one to seven and it gives an introduction to several issues which are essential prior to solve problems in computational non-Newtonian fluid mechanics. This part of the book deals with the derivation of viscoelastic flow equations, the construction of stress constitutive models, the mathematical theory of partial differential equations, and the essential elements of discretization techniques and numerical algorithms for solving viscoelastic flow equations. This first part of the book has been written to be as self-contained as possible. In the first chapter the reader is introduced to the Maxwell model, the Kelvin model, and to the behavior of non-Newtonian liquids in shear and uniaxial elongational flow. Furthermore, Chap. 1 explores some of the reasons for the high Weissenberg number problem a key issue in computational rheology and how innovative techniques have been devised to solve/circumvent it. The second chapter consists of two main parts: First the definition of several kinematic quantities are given and some fundamental results in fluid mechanics are derived, then constitutive relationships for the stress tensor are introduced. Readers being interested in a more in-depth study of the mathematics of viscoelasticity, the description of experimental studies of viscoelasticity viz. rheometry, and the microstructural modeling of polymeric liquids (cf. also Chap. 11) are referred to alternative textbooks. The subsequent Chap. 3 deals with the mathematical properties of the underlying viscoelastic flow equations: existence and uniqueness of the solutions of the flow equations, specification of boundary conditions, and the presence of singularities at some locations of the flow domain (such as corners or edges). The following Chap. 4 addresses the difficulties in choosing appropriate constitutive equations for the extra stress tensor to achieve agreement of computer simulations with experimentally observed properties of viscoelastic liquids. Furthermore, the characterization of viscoelastic fluids in terms of basic material functions and the problem of phenomenological parameter entering the flow equations are addressed. Chap. 5 and 6 deal with the discretization of viscoelastic flow equations and the numerical solution of the discretized equations, respectively. Chap. 6 treats a variety of different solution methods such as finite difference methods, Galerkin finite element methods, finite volume methods, and specApplied Rheology Vol.12/6.qxd 10.01.2003 13:58 Uhr Seite 280