| Description |
1 online resource |
| Contents |
Front Cover; Dedication ; Stable Numerical Schemes for Fluids, Structures and their Interactions; Copyright ; Contents; Preface; 1. Mixed Finite Elements for the Stokes Equations; 1.1. Stokes equations; 1.2. Existence and uniqueness for an abstract mixed problem; 1.3. Existence and uniqueness for the Stokes equations; 1.4. Finite element approximation of an abstract mixed problem; 1.5. Mixed finite elements for the Stokes equations; 1.6. Boundary conditions for the Stokes equations; 1.7. Numerical tests; 2. Numerical Schemes for the Navier-Stokes Equations; 2.1. Navier-Stokes equations |
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2.2. Implicit Euler scheme, semi-implicit treatment of the nonlinear term2.3. Implicit Euler scheme and implicit treatment of the nonlinear term; 2.4. Implicit Euler scheme and explicit treatment of the nonlinear term; 2.5. Some properties of the trilinear forms c and ˜c; 2.6. Numerical tests: flow around a disc; 3. The ALE Method for Navier-Stokes Equations in a Moving Domain; 3.1. Lagrangian and Eulerian coordinates; 3.2. Arbitrary Lagrangian Eulerian (ALE) coordinates; 3.3. Weak non-conservative and conservative formulations |
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3.4. Discretization of order one in time for the weak conservative formulation3.5. Stabilized discretization of order one in time for the non-conservative formulation; 3.6. Finite element discretization in space; 3.7. Numerical tests; 4. Linear Elastodynamics; 4.1. Two-dimensional linear elasticity; 4.2. Abstract formulation; 4.3. Backward Euler scheme; 4.4. Implicit centered scheme; 4.5. Mid-point scheme; 4.6. Numerical tests; 5. Nonlinear Elastodynamics; 5.1. Total Lagrangian formulation; 5.2. The St Venant-Kirchhoff model; 5.3. Total Lagrangian backward Euler scheme |
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5.4. Total Lagrangian mid-point scheme5.5. Numerical tests; 6. Numerical Schemes for the Fluid-Structure Interaction; 6.1. Non-conservative and conservative weak formulations; 6.2. Discretization in time of the conservative form: implicit domain calculation; 6.3. Discretization in time of the non-conservative form: explicit domain calculation; 6.4. Coupling strategies; 6.5. The constants in the Poincaré, Korn and trace inequalities; 6.6. Numerical tests; Appendix: Functional Analysis Tools; A.1. Sobolev spaces; A.2. Closed, surjective operators; Bibliography; Index; Back Cover |
| Summary |
This book presents numerical algorithms for solving incompressible fluids, elastic structures and fluid-structure interactions. It collects some of the fundamental finite element methods as well as new approaches. For Stokes and Navier-Stokes equations, the mixed finite element method is employed. An arbitrary Lagrangian Eulerian framework is used for fluids in a moving domain. Schemes for linear and St Venant-Kirchhoff non-linear dynamic elasticity are presented. For fluid-structure interaction, two schemes are analyzed: the first is fully implicit and the second is semi-implicit, where the fluid domain is computed explicitly and consequently the computational time is considerably reduced. The stability of the schemes is proven in this self-contained book. Every chapter is supplied with numerical tests for the reader. These are aimed at Masters students in Mathematics or Mechanical Engineering |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed September 13, 2017) |
| Subject |
Numerical analysis.
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Differential equations, Partial -- Numerical solutions.
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Navier-Stokes equations -- Numerical solutions.
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Group schemes (Mathematics)
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Fluid-structure interaction.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Differential equations, Partial -- Numerical solutions
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Fluid-structure interaction
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Group schemes (Mathematics)
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Navier-Stokes equations -- Numerical solutions
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Numerical analysis
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| Form |
Electronic book
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| ISBN |
9780081023808 |
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0081023804 |
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