Numerical Simulation of Non-Newtonian Flow

PrefaceSection 1 : Non-Newtonian Fluid Mechanics 1. General Introduction 1.1 Introduction 1.2 Rheometrical Properties of Non-Newtonian Fluids 1.3 Non-Newtonian Flow in Complex Geometries 1.4 The Role of Non-Newtonian Fluid Mechanics 2. Basic Equations 2.1 Introduction 2.2 Field Equations 2.3 Navier Stokes Equations 2.4 Rheological Equations of State. Formulation Principles 2.5 The Simple Fluid 2.6 Approximate Constitutive Equations 2.7 A Pragmatic Approach to Constitutive Equations 2.8 Constraints on Rheological Equations of State 2.9 Boundary Conditions Appendix I 3. Flow Classification 3.1 Introduction 3.2 Flows Dominated by Shear Viscosity 3.3 Slow Flow (Slightly Elastic Liquids) 3.4 Small-Deformation Flows 3.5 Nearly-Viscometric Flows 3.6 Highly Elastic Liquids Flowing in Complex Geometries 3.7 General Comments Concerning Flows Involving Abrupt Changes in Geometry 3.8 Some Remarks on Non-Dimensional Parameters 3.9 Basic Equations for the Flow of a Maxwell Fluid 4. An Overview of Numerical Simulation 4.1 Introduction 4.2 Step 1 : Formulating the Governing Equations and Boundary Conditions 4.3 Step 2 : Time Discretization 4.4 Step 3 : Space Discretization 4.5 Step 4 : Linearization 4.6 Step 5 : Solution of the Linearization Equation 4.7 Step 6 : Termination of the Nonlinear Iteration LoopSection 2 : Finite Difference Techniques 5. Introduction to Finite Differences 5.1 Boundary Value Problems in One and Two Space Dimensions 5.2 Finite Difference Solution of Two-Point Boundary Value Problems: The Linear Case 5.3 Finite Difference Solution of Two-Point Boundary Value Problems: The Nonlinear Case 5.4 Finite Difference Solution of Elliptic Boundary Value Problems: Poisson's Equation 6. Finite Difference Simulation : Differential Models 6.1 Introduction 6.2 Discretization 6.3 Solution of Linear Equations 6.4 Solution of Coupled Systems 6.5 Examples 6.6 Miscellaneous Topics 7. Finite Difference Simulation ; Time Dependence 7.1 Introduction 7.2 Unsteady Flows 7.3 Integral Constitutive ModelsSection 3 : Finite Element Techniques 8. Introduction to Finite Elements 8.1 Introduction 8.2 Finite Element Representation 8.3 The Finite Element Method 8.4 Method of Weighted Residuals 8.5 Construction of the Algebraic System 8.6 Solution of the Algebraic System 8.7 Examples 8.8 Two-Dimensional Problems. Triangular and Rectangular Elements 8.9 Isoparametric Elements 8.10 Method of Weighted Residuals 8.11 Numerical Integration 8.12 Example. Convergence of the Finite Element Method 9. Finite Element Calculation of Generalized Newtonian Flow 9.1 Introduction 9.2 A Variational Theorem for Creeping Generalized Newtonian Flow 9.3 Galerkin Formulation of the Equations of Motion; Plane Flow 9.4 Galerkin Formulation of the Equations of Motion; Axisymmetric Flow 9.5 Finite Elements for Solving the Navier-Stokes Equations 9.6 Penalty Formulation for Solving the Navier-Stokes Equations 9.7 Calculation of the Stream Function 9.8 Solving the Generalized Newtonian Flow 9.9 Entry Flow in a Tubular Contraction 9.10 Die Swell of a Generalized Newtonian Fluid 9.11 The Flow of a Power-Law Fluid Around a Sphere 10. Finite Element Calculation of Viscoelastic Flow 10.1 Introduction 10.2 Another Variational Theorem for Creeping Newtonian Flow 10.3 A Mixed Method for Solving the Stokes Equations 10.4 A Mixed Method for Solving the Flow of a Maxwell Fluid (MIX1) 10.5 A Second Mixed Method for Solving the Flow of a Maxwell Fluid (MIX2, MIX3) 10.6 Axisymmetric Flow 10.7 Problems with the Mixed Methods 10.8 The Oldroyd-B Fluid and Related Models 10.9 A Third Method for Solving the Flow of a Maxwell Fluid (MIX4) 10.10 The Flow of Viscoelastic Fluids of the Integral Type 10.11 Example of the General Development - Entry Flow in a Tubular Contraction 10.12 Example of the General Development - Die Swell of a Viscoelastic Fluid 10.13 Related ProblemsSection 4 : Epilogue 11. Outstanding Problems. Future Trends 11.1 General 11.2 Numerical Simulation Breakdown 11.3 Possible Reasons for Breakdown : An Evaluation 11.4 Concluding RemarksReferencesAuthor IndexSubject Index