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.Contents: IntroductionFundamentalsMathematical Theory of Viscoelastic FluidsParameter Estimation in Continuum ModelsFrom the Continuous to the DiscreteNumerical Algorithms for Macroscopic ModelsDefeating the High Weissenberg Number ProblemBenchmark Problems I: Contraction FlowsBenchmark Problems IIError Estimation and Adaptive StrategiesContemporary Topics in Computational RheologyReadership: Advanced undergraduate and graduate students, researchers and academics with an interest in computational solutions to rheological flow problems.