This book presents the stream-tube method (STM), a method offering computational means of dealing with the two- and three-dimensional properties of numerous incompressible materials in static and dynamic conditions. The authors show that the kinematics and stresses associated with the flow and deformation in such materials can be treated by breaking the system down into simple computational sub-domains in which streamlines are straight and parallel and using one or two mapping functions in steady-state and non-steady-state conditions.
The STM is considered for various problems in non-Newtonian fluid mechanics with different geometries. The book makes use of examples and applications to illustrate the use of the STM. It explores the possibilities of computation on simple mapped rectangular domains and three-dimensional parallel-piped domains under different conditions. Complex materials with memory are considered simply without particle tracking problems.
Readers, including researchers, engineers and graduate students, with a foundational knowledge of calculus, linear algebra, differential equations and fluid mechanics will benefit most greatly from this book.
Table of Contents:
1. Tensors-Frames.- 2. Kinematics – Conservation Laws, Constitutive Equations.- 3. Domain Transformations – Stream-Tube Method in Two-dimensional Cases.- 4. Stream-Tube Method in Two-dimensional Problems.- 5. Stream-Tube Method in Three-dimensional Problems.
About the Author :
Dr. Jean-Robert Clermont has been Emeritus Research Director at CNRS (National Centre for Scientific Research, France) since 2010 and continues to collaborate with the Laboratoire Rhéologie et Procédés de Grenoble, CNRS/Université Grenoble Alpes (UGA)/Institut National Polytechnique de Grenoble (INP Grenoble). He is Civil Engineer, has obtained a master's degree in Applied Mathematics and a Ph D. and presented a State Thesis, at Grenoble University. He has taught Continuum Mechanics, Mathematics and Computational Methods at a master's level.
His research focuses on theory, applications and numerical simulations in the field of rheology. He proposed the so-called stream-tube method, in connection with problems encountered in nonlinear behavior of materials. Dr. Clermont has advised more than 30 students in Ph.D. and master's degrees. He has presented plenary talks at international conferences and has published research results in high-level international periodicals.
Professor Amine Ammar is Full Professor of Computational Mechanics at Arts & Métiers Paris Tech. He obtained his Ph.D. Thesis in 2001 at the Paris VI University - ENS Cachan. In 2006, he obtained his French degree to supervise research (HdR), with a specialty in mechanics. In 2009, he was awarded the Scientific prize of the European Association of Material Forming awarded in the 12th Esaform Conference and the French Jean Mandel prize awarded in the 19th CFM Conference. His research has been on various topics: model reduction of PDE resolution, proper generalized decomposition, kinetic theory of polymers and suspensions and short reinforced fiber composite processing, among them.
