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Stable numerical schemes for fluids, structures and their interactions /
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. A...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London : Oxford, UK :
ISTE Press Ltd ; Elsevier Ltd,
2017.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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
- 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.
- 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 Poincar�e, 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.