Details

Subject(s)

• Fluid-structure interaction [Browse]
• Level set methods [Browse]

Author

• Maitre, Emmanuel [Browse]
• Milcent, Thomas [Browse]

Series

• Applied mathematical sciences (Springer-Verlag New York Inc.) ; Volume 210. [More in this series]
• Applied mathematical sciences ; Volume 210

Bibliographic references

Includes bibliographical references.

Source of description

Description based on print version record.

Contents

• Intro
• Foreword
• Contents
• 1 Level Set Methods and Lagrangian Interfaces
• 1.1 Interface Tracking or Interface Capturing
• 1.2 Level Set Methods and Geometry of Surfaces
• 1.3 Level Set Methods and Geometry of Curves in R3
• 1.4 Expression of Surface Forces Using the Level Set Function
• 1.4.1 Example 1: Image Processing
• 1.4.2 Exemple 2: Surface Tension
• 1.5 Numerical Aspects I: Consistency and Accuracy
• 1.5.1 Redistancing of φ
• 1.5.2 Renormalization of φ
• 1.5.3 Comparison of the Two Approaches
• 1.5.4 Towers Method to Approximate Surface Integrals
• 1.6 Numerical Aspects II: Stability
• 1.6.1 Explicit Scheme
• 1.6.2 Implicit Scheme
• 1.6.3 Semi-Implicit Scheme
• 2 Mathematical Tools for Continuum Mechanics
• 2.1 Characteristics and Flows Associated with a Velocity Field
• 2.2 Change of Variables
• 2.3 Reynolds Formulas
• 2.4 Conservation of Mass
• 2.4.1 Mass Conservation in Eulerian Formulation
• 2.4.2 Mass Conservation in Lagrangian Formulation
• 2.5 Conservation of Momentum
• 2.5.1 Momentum Conservation in Eulerian Formulation
• 2.5.2 Momentum Conservation in Lagrangian Formulation
• 3 Interaction of an Incompressible Fluid with an Elastic Membrane
• 3.1 From the Immersed Boundary Method to Level Set Methods
• 3.2 Immersed Membrane: Case Without Shear
• 3.2.1 Level Set Formulation of the Elastic Deformation of a Hypersurface Immersed in a Incompressible Fluid
• 3.2.2 Level Set Formulation of Elastic Energy and Fluid-Structure Coupling in the Incompressible Case
• 3.2.3 Generalization to Compressible Flows
• 3.2.4 Taking into Account Curvature Forces
• 3.2.5 Korteweg Models and Existence of Solutions
• 3.3 Immersed Membrane: The Case with Surface Shear
• 3.3.1 Level Set Approach for Surfaces
• 3.3.2 An Eulerian Tensor to Measure Surface Deformation
• 3.3.3 Invariants and Associated Elastic Force.
• 3.3.4 Energy and Coupling Model
• 3.4 Curves Immersed in R3
• 3.4.1 An Eulerian Tensor to Measure Strains Along Curves
• 3.4.2 Invariants and Associated Elastic Force
• 3.5 Explicit and Semi-implicit Time Discretizations
• 3.5.1 Explicit Schemes
• 3.5.2 Semi-implicit Scheme
• 3.5.3 Numerical Validation
• 3.6 Numerical Illustrations and Sample Code
• 3.6.1 Shear-Free Membrane
• 3.6.1.1 2D Oscillating Elastic Membrane: FreeFEM++ and Matlab Codes
• 3.6.1.2 Membrane with Bending Energy
• 3.6.2 Membrane with Shear
• 4 Immersed Bodies in a Fluid: The Case of Elastic Bodies
• 4.1 Hyperelastic Materials in Lagrangian Formulation
• 4.1.1 Principle of Material Indifference
• 4.1.2 Isotropic Materials
• 4.1.3 Computation of the Stress Tensor in a Lagrangian Framework
• 4.2 Hyperelastic Materials in Eulerian Formulation
• 4.2.1 Computation of the Stress Tensor in an Eulerian Framework
• 4.2.2 Elastic Constitutive Laws for Elastic Media
• 4.2.3 Eulerian Elasticity in the Incompressible Case
• 4.2.4 Eulerian Elasticity in the Compressible Case
• 4.3 Fluid-Structure Coupling Model in the Incompressible Case
• 4.3.1 Model and Constitutive Law in the Incompressible Case
• 4.3.2 Numerical Illustrations
• 4.3.2.1 Elastic Ball in a Driven Cavity
• 4.3.2.2 Flapping of an Elastic Rod
• 4.3.2.3 Wave Damping by Elastic Structures
• 4.3.2.4 Fluid-Structure Interaction in the Contraction of a Cardiac Muscle Cell
• 4.4 Fluid-Structure Coupling in the Compressible Case
• 4.4.1 Model and Constitutive Law in the Compressible Case
• 4.4.2 Numerical Scheme
• 4.4.3 Numerical Illustration
• 5 Immersed Bodies in Incompressible Fluids: The Case of Rigid Bodies
• 5.1 The Penalization Method for Flow Around Bodies with Given Velocity
• 5.2 The Case of the Two-Ways Fluid-Solid Interaction
• 5.3 Remarks on the Numerical Implementation.
• 5.4 Extensions of the Penalization Method
• 5.5 Numerical Illustrations
• 5.5.1 Kissing and Tumbling of Two Spheres
• 5.5.2 Flows Around Oscillating Obstacles
• 5.5.3 Anguilliform Swimmers
• 6 Computing Interactions Between Solids by Level Set Methods
• 6.1 Level Set Method to Model Interaction Forces
• 6.1.1 Point Repulsion Model
• 6.1.2 Surface Repulsion Model by Level Set Method
• 6.1.3 Taking into Account Cohesion and Damping Forces
• 6.1.4 Numerical Illustrations
• 6.2 An Efficient Method for Dealing with Contacts Between Multiple Objects
• 6.2.1 Motivation
• 6.2.2 The Algorithm
• 6.2.2.1 Label Functions
• 6.2.2.2 Distance Functions
• 6.2.2.3 Dealing with Contact Forces
• 6.2.2.4 Penalization and Complete Model
• 6.2.3 Computational Efficiency of the Method
• 6.2.4 Numerical Illustrations
• 7 Annex
• 7.1 Examples of Curvature Calculations Using a Level Set Function
• 7.1.1 The Case of the Ellipsoid
• 7.1.2 The Case of the Torus
• 7.2 Justification of the Results Used for Membranes with Shear
• 7.2.1 Proof of the Results Concerning the Z1 Invariant
• 7.2.2 Analytical Illustrations for Z2
• 7.3 Justification of the Results Used for the Curves Parameterized in R3
• 7.3.1 Proof of the Results Concerning the Invariant Z3
• 7.3.2 Area and Co-area Formulas
• 7.3.3 Volume Approximation of Line Integrals and Calculation of the Elastic Force
• 7.4 WENO Schemes for the Transport Equation
• 7.5 Some Ideas to Go Further
• Credits of Figures Reproduced with Permission
• References.

Show 111 more Contents items

ISBN

9783031086595 ((electronic bk.))

Statement on language in description

Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...