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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 |
|---|---|
| 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 |
MARC
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| 100 | 1 | |a Murea, Cornel Marius, |e author. | |
| 245 | 1 | 0 | |a Stable numerical schemes for fluids, structures and their interactions / |c Cornel Marius Murea. |
| 264 | 1 | |a London : |b ISTE Press Ltd ; |a Oxford, UK : |b Elsevier Ltd, |c 2017. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed September 13, 2017). | |
| 520 | |a 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. | ||
| 650 | 0 | |a Numerical analysis. | |
| 650 | 0 | |a Differential equations, Partial |x Numerical solutions. | |
| 650 | 0 | |a Navier-Stokes equations |x Numerical solutions. | |
| 650 | 0 | |a Group schemes (Mathematics) | |
| 650 | 0 | |a Fluid-structure interaction. | |
| 650 | 6 | |a Analyse num�erique. |0 (CaQQLa)201-0021900 | |
| 650 | 6 | |a �Equations aux d�eriv�ees partielles |x Solutions num�eriques. |0 (CaQQLa)201-0041240 | |
| 650 | 6 | |a �Equations de Navier-Stokes |x Solutions num�eriques. |0 (CaQQLa)201-0085176 | |
| 650 | 6 | |a Sch�emas en groupes. |0 (CaQQLa)201-0020978 | |
| 650 | 6 | |a Interaction fluide-structure. |0 (CaQQLa)201-0277017 | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Partial |x Numerical solutions. |2 fast |0 (OCoLC)fst00893488 | |
| 650 | 7 | |a Fluid-structure interaction. |2 fast |0 (OCoLC)fst00928031 | |
| 650 | 7 | |a Group schemes (Mathematics) |2 fast |0 (OCoLC)fst00948511 | |
| 650 | 7 | |a Navier-Stokes equations |x Numerical solutions. |2 fast |0 (OCoLC)fst01035075 | |
| 650 | 7 | |a Numerical analysis. |2 fast |0 (OCoLC)fst01041273 | |
| 776 | 0 | 8 | |i Print version: |a Murea, Cornel Marius. |t Stable numerical schemes for fluids, structures and their interactions. |d London : ISTE Press Ltd ; Oxford, UK : Elsevier Ltd, 2017 |z 1785482734 |z 9781785482731 |w (OCoLC)983459760 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9781785482731 |z Texto completo |