Stream-tube method : a complex-fluid dynamics and computational approach / / Jean-Robert Clermont, Amine Ammar

• Autore: Clermont Jean-Robert
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (303 pages)
• Disciplina: 530.42
• Soggetto topico: Complex fluids; Fluid dynamics - Mathematical models; Computational fluid dynamics
• Persona (resp. second.): AmmarAmine
• Nota di contenuto: Intro -- Foreword -- Acknowledgements -- Introduction -- Specific Features of the Book -- Examples in the Book -- Expected Audience -- Pathways Through the Book -- Contents -- Nomenclature -- Abbreviations -- Notation -- 1 Tensor Frames -- 1.1 Introduction -- 1.2 Matrices -- 1.3 Vectors and Basis -- 1.3.1 Vectors in Cartesian Coordinates -- 1.3.2 Basis Vectors -- 1.3.3 Natural Basis: Dual of Natural Basis -- 1.3.4 Contravariant and Covariant Components -- 1.3.5 Change of Coordinates -- 1.3.6 Vector Matrix -- 1.3.7 Gradient of a Scalar Function -- 1.4 Tensors -- 1.4.1 Tensor Operations -- 1.4.2 Invariants of Second-Order Tensors -- 1.5 Operations with Derivatives -- 1.5.1 Gradients -- 1.5.2 Divergence -- 1.5.3 Curl of a Vector -- 1.6 Special Non-Cartesian Coordinate Systems -- 1.6.1 Cylindrical Coordinates -- 1.6.2 Spherical Coordinates -- References -- 2 Kinematics-Conservation Laws: Constitutive Equations -- 2.1 Introduction -- 2.2 Kinematics -- 2.2.1 Basic Elements: Eulerian and Lagrangian Descriptions: Material Derivative -- 2.2.2 Kinematic Tensors -- 2.2.3 Stress Tensor-Stress Vector -- 2.3 Laws of Conservation -- 2.3.1 Mass Conservation: Incompressible Materials -- 2.4 Momentum Conservation Equations -- 2.4.1 Linear Momentum Equation -- 2.4.2 Conservation of Angular Momentum -- 2.5 Conservation of Energy -- 2.6 Constitutive Equations -- 2.6.1 Inelastic Models: Newtonian Fluid -- 2.6.2 Viscoelastic Constitutive Equations -- 2.7 Concluding Remarks -- References -- 3 Domain Transformations: Stream-Tube Method in Two-Dimensional Cases -- 3.1 Introduction -- 3.2 Global Transformations for Physical Domains -- 3.2.1 Conformal Mappings-Grid Generation Techniques -- 3.2.2 General Curvilinear Coordinates -- 3.2.3 Domain Transformations Based on Kinematic Concepts -- 3.3 Stream-Tube Method (STM) for Two-Dimensional Problems. ; 3.3.1 Transformation for Two-Dimensional Domains -- 3.3.2 Basic Operators -- 3.3.3 Natural and Reciprocal Bases with Curvilinear Coordinates -- 3.3.4 Deformation Gradient Tensor -- 3.4 Velocity Gradient, Rate-of-Deformation and Vorticity Tensors in Two-Dimensional Cases -- 3.4.1 The Planar Case -- 3.4.2 The Axisymmetric Case -- 3.4.3 Velocity Derivatives Versus the Mapping Functions -- 3.4.4 Momentum Conservation Equations in 2D Isothermal Cases -- 3.4.5 Specific Features in Stream-Tube Method -- 3.5 Stream-Tube Method and Constitutive Equations -- 3.5.1 Newtonian and Inelastic Rheological Models -- 3.5.2 Differential Models -- 3.5.3 Memory-Integral Models -- 3.6 Concluding Remarks -- References -- 4 Stream-Tube Method in Two-Dimensional Problems -- 4.1 Introduction -- 4.2 Formulations: Boundary Conditions -- 4.2.1 Primary and Mixed Formulations -- 4.2.2 Boundary Condition Equations -- 4.3 Discretization -- 4.3.1 Approximating the Unknowns -- 4.3.2 Finite Differences -- 4.3.3 Mesh Elements -- 4.4 Solving the Equations -- 4.4.1 Consistency and Stability -- 4.4.2 The Newton-Raphson Algorithm -- 4.4.3 Methods Based on Optimization Concepts-Trust Region Algorithm -- 4.4.4 Levenberg-Marquardt (LM) Optimization Algorithm -- 4.5 Two-Dimensional Flows -- 4.5.1 Flow Rates and Streamlines in a Tube -- 4.5.2 Inelastic Models: Newtonian Examples -- 4.5.3 Viscoelastic Models in STM Problems -- 4.6 Concluding Remarks -- 4.7 Examples of Two-Dimensional Flow Situations for STM -- References -- 5 Stream-Tube Method in Three-Dimensional Problems -- 5.1 Introduction -- 5.2 Analysis of Three-Dimensional Flows -- 5.2.1 Basic Equations -- 5.2.2 Determination of Velocity Contour Curves in Poiseuille Flows -- 5.2.3 Computations of Kinematics -- 5.2.4 Conservation Laws and Boundary Conditions -- 5.2.5 Boundary Condition Equations. ; 5.2.6 The Transformation in Cylindrical Coordinates -- 5.2.7 Dynamic Equations with Cylindrical Coordinates -- 5.2.8 Kinematic Tensors for Codeformational Models -- 5.3 STM Applications -- 5.3.1 Newtonian Fluid in a Converging Domain -- 5.3.2 Viscoelastic Fluid in the Converging Domain -- 5.3.3 Swell Problem: Duct of Square Cross-Section -- 5.4 Concluding Remarks -- 5.5 Example of a Three-Dimensional Problem in STM -- References -- 6 Stream-Tube Method Domain Decomposition Closed Streamlines -- 6.1 Introduction -- 6.2 General Transformations: Basic Computational Results with the Stream-Tube Method -- 6.2.1 Basic Equations for General Transformations -- 6.2.2 Transformations of Sub-domains -- 6.2.3 Kinematics: Basic Equations and Unknowns -- 6.3 Specific Properties: Computational Considerations -- 6.3.1 Specific Features of the Analysis -- 6.3.2 Reference Kinematic Functions: Computational Considerations -- 6.4 Flows in Ducts -- 6.5 Flows Between Eccentric Cylinders -- 6.5.1 Rotating Flows Without Recirculations: An Example -- 6.5.2 Two-Dimensional Flows Between Eccentric Cylinders (Journal Bearing Problem) with Recirculating Regions -- 6.6 Concluding Remarks -- References -- 7 Stream-Tube Method for Unsteady Flows -- 7.1 Introduction -- 7.2 Theoretical Analysis of Unsteady Flows in STM -- 7.2.1 Open and Closed Streamlines -- 7.2.2 Domain Transformation of Open Streamlines in Unsteady Flows -- 7.2.3 Domain Transformation for Unsteady Flows with Closed Streamlines -- 7.3 Examples: Flows Between Concentric and Eccentric Cylinders for Newtonian, Anelastic and Viscoelastic Fluids -- 7.3.1 Flow Characteristics: Rheological Models for the Applications -- 7.3.2 Dynamic Equations and Solving Procedure -- 7.3.3 Numerical Results -- 7.4 Concluding Remarks -- References -- 8 Stream-Tube Method for Thermal Flows and Solid Mechanics -- 8.1 Introduction. ; 8.2 Thermal Flows in Stream-Tube Method -- 8.2.1 Stream-Tube Method and the Thermal Problem -- 8.2.2 Energy Equation with Finite Element Approach -- 8.2.3 Two-Dimensional Examples: Ducts with Restriction Zones: Stick-slip: Converging Flows -- 8.3 Comments on the STM Flow Results -- 8.4 Stream-Tube Method for Solid Mechanics Problems -- 8.4.1 Formulation Based on Energetic Concepts -- 8.4.2 An Example of Results -- 8.5 Concluding Remarks -- References -- 9 Micro-Macro Simulations and Stream-Tube Method -- 9.1 Introduction -- 9.2 A Representative Micro-Macro Model of a Complex Fluid Flow -- 9.2.1 Macroscopic Equations -- 9.2.2 Microscopic Equations of a Hypothetical Fibre Network Model -- 9.3 Microscopic Scale: A Separated Representation Solver -- 9.3.1 Addressing Complex Flows -- 9.4 Macroscopic Scale: Flow Kinematics Solver -- 9.4.1 The Stream-Tube Method Revisited: Basic Concepts -- 9.4.2 Solving the Problem -- 9.5 Numerical Results -- 9.5.1 Transient Network Analysis in a Steady Simple Shear -- 9.5.2 Analysis of a Contraction Flow -- 9.5.3 Convergence Analysis -- 9.6 Concluding Remarks -- References -- Appendix A4.1 Detailed Coefficients for Differential Equations -- Appendix A9.1 Separated Representation Solver: Notation -- Appendix A9.2 Separated Representation Solver: Projection Step -- Appendix A9.3 Separated Representation Solver: Approximation Basis Enrichment -- Index.
• Titolo autorizzato: Stream-tube method
• ISBN: 3-030-65470-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910484564903321
• Lo trovi qui: Univ. Federico II