Computational rheology

Modern day high-performance computers are making available to 21st-century scientists solutions to rheological flow problems of ever-increasing complexity. Computational rheology is a fast-moving subject - problems which only 10 years ago were intractable, such as 3D transient flows of polymeric liquids, non-isothermal non-Newtonian flows or flows of highly elastic liquids through complex geometries, are now being tackled owing to the availability of parallel computers, adaptive methods and advances in constitutive modelling. Computational Rheology traces the development of numerical methods for non-Newtonian flows from the late 1960's to the present day. It begins with broad coverage of non-Newtonian fluids, including their mathematical modelling and analysis, before specific computational techniques are discussed. The application of these techniques to some important rheological flow problems of academic and industrial interest is then treated in a detailed and up-to-date exposition. Finally, the reader is kept abreast of topics at the cutting edge of research in computational applied mathematics, such as adaptivity and stochastic partial differential equations. All the topics in this book are dealt with from an elementary level and this makes the text suitable for advanced undergraduate and graduate students, as well as experienced researchers from both the academic and industrial communities.

1. Introduction. 1.1. Everything flows. 1.2. Non-Newtonian fluids. 1.3. Numerical simulation of non-Newtonian flow -- 2. Fundamentals. 2.1. Some important vectors. 2.2. Conservation laws and the stress tensor. 2.3. The Newtonian fluid. 2.4. The generalized Newtonian fluid. 2.5. The order fluids and the CEF equation. 2.6. More complicated constitutive relations -- 3. Mathematical theory of viscoelastic fluids. 3.1. Introduction. 3.2. Existence and uniqueness. 3.3. Properties of the differential systems. 3.4. Boundary conditions. 3.5. Singularities -- 4. Parameter estimation in continuum models. 4.1. Introduction. 4.2. Determination of viscosity. 4.3. Determination of the relaxation spectrum -- 5. From the continuous to the discrete. 5.1. Introduction. 5.2. Finite difference approximations. 5.3. Finite element approximations. 5.4. Finite volume methods. 5.5. Spectral methods. 5.6. Spectral element methods -- 6. Numerical algorithms for macroscopic models. 6.1. Introduction. 6.2. Prom Picard to Newton. 6.3. Differential models: steady flows. 6.4. Differential models: transient flows. 6.5. Computing with integral models. 6.6. Integral models: steady flows. 6.7. Integral models: transi…