Numerical Methods for Non-Newtonian Fluids: Special Volume

Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume’s articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike.

This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics.

New review of well-known computational methods for the simulation viscoelastic and viscoplastic typesDiscusses new numerical methods that have proven to be more efficient and more accurate than traditional methodsArticles that discuss the numerical simulation of particulate flow for viscoelastic fluids

Part I: Grade-Two Fluids Numerical Methods for Grade-Two Fluid Models: Finite-element Discretizations and Algorithms

Part II: Viscoelastic Fluids The Langevin and Fokker-Planck Equations in Polymer Rheology Viscoelastic Flows with Complex Free Surfaces: Numerical Analysis and Simulation Stable Finite Element Discretizations for Viscoelastic Flow Models Positive Definiteness Preserving Approaches for Viscoelastic Flow of Oldroyd-B Fluids: Applications to a Lid-driven Cavity Flow and a Particulate Flow

Part III: Viscoplastic Fluids On the Numerical Simulation of Viscoplastic Fluid Flows Modeling, Simulation and Optmization of Electrorheological Fluids