Navier-Stokes equations in planar domains:
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
c2013
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 287-297) and index Pt. I. Basic theory. 1. Introduction. 1.1. Functional notation -- 2. Existence and uniqueness of smooth solutions. 2.1. The linear convection-diffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2 -- 3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3 -- 4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4 -- 5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5 -- 6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6 -- - A. Some theorems from functional analysis. A.1. The Calderón-Zygmund theorem. A.2. Young's and the Hardy-Littlewood-Sobolev inequalities. A.3. The Riesz-Thorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel -- pt. II. Approximate solutions. 7. Introduction -- 8. Notation. 8.1. One-dimensional discrete setting. 8.2. Two-dimensional discrete setting -- 9. Finite difference approximation to second-order boundary-value problems. 9.1. The principle of finite difference schemes. 9.2. The three-point Laplacian. 9.3. Matrix representation of the three-point Laplacian. 9.4. Notes for chapter 9 -- - 10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The three-point biharmonic operator. 10.4. Accuracy of the three-point biharmonic operator. 10.5. Coercivity and stability properties of the three-point biharmonic operator. 10.6. Matrix representation of the three-point biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10 -- 11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11 -- 12. Compact approximation of the Navier-Stokes equations in streamfunction formulation. 12.1. The Navier-Stokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12 -- - B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation -- 13. Fully discrete approximation of the Navier-Stokes equations. 13.1. Fourth-order approximation in space. 13.2. A time-stepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13 -- 14. Numerical simulations of the driven cavity problem. 14.1. Second-order scheme for the driven cavity problem. 14.2. Fourth-order scheme for the driven cavity problem. 14.3. Double-driven cavity problem. 14.4. Notes for chapter 14 This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "double-driven cavity". A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics |
| Beschreibung: | 1 Online-Ressource (xii, 302 p.) |
| ISBN: | 1848162766 9781848162754 9781848162761 |
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| 245 | 1 | 0 | |a Navier-Stokes equations in planar domains |c Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov |
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| 500 | |a Includes bibliographical references (p. 287-297) and index | ||
| 500 | |a Pt. I. Basic theory. 1. Introduction. 1.1. Functional notation -- 2. Existence and uniqueness of smooth solutions. 2.1. The linear convection-diffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2 -- 3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3 -- 4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4 -- 5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5 -- 6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6 -- | ||
| 500 | |a - A. Some theorems from functional analysis. A.1. The Calderón-Zygmund theorem. A.2. Young's and the Hardy-Littlewood-Sobolev inequalities. A.3. The Riesz-Thorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel -- pt. II. Approximate solutions. 7. Introduction -- 8. Notation. 8.1. One-dimensional discrete setting. 8.2. Two-dimensional discrete setting -- 9. Finite difference approximation to second-order boundary-value problems. 9.1. The principle of finite difference schemes. 9.2. The three-point Laplacian. 9.3. Matrix representation of the three-point Laplacian. 9.4. Notes for chapter 9 -- | ||
| 500 | |a - 10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The three-point biharmonic operator. 10.4. Accuracy of the three-point biharmonic operator. 10.5. Coercivity and stability properties of the three-point biharmonic operator. 10.6. Matrix representation of the three-point biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10 -- 11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11 -- 12. Compact approximation of the Navier-Stokes equations in streamfunction formulation. 12.1. The Navier-Stokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12 -- | ||
| 500 | |a - B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation -- 13. Fully discrete approximation of the Navier-Stokes equations. 13.1. Fourth-order approximation in space. 13.2. A time-stepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13 -- 14. Numerical simulations of the driven cavity problem. 14.1. Second-order scheme for the driven cavity problem. 14.2. Fourth-order scheme for the driven cavity problem. 14.3. Double-driven cavity problem. 14.4. Notes for chapter 14 | ||
| 500 | |a This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "double-driven cavity". A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics | ||
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Datensatz im Suchindex
| _version_ | 1804175521560395776 |
|---|---|
| any_adam_object | |
| author | Ben-Artzi, Matania |
| author_facet | Ben-Artzi, Matania |
| author_role | aut |
| author_sort | Ben-Artzi, Matania |
| author_variant | m b a mba |
| building | Verbundindex |
| bvnumber | BV043106396 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)844311053 (DE-599)BVBBV043106396 |
| dewey-full | 532.05201515353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.05201515353 |
| dewey-search | 532.05201515353 |
| dewey-sort | 3532.05201515353 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043106396 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:37Z |
| institution | BVB |
| isbn | 1848162766 9781848162754 9781848162761 |
| language | English |
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| physical | 1 Online-Ressource (xii, 302 p.) |
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| publisher | Imperial College Press |
| record_format | marc |
| spelling | Ben-Artzi, Matania Verfasser aut Navier-Stokes equations in planar domains Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov London Imperial College Press c2013 1 Online-Ressource (xii, 302 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 287-297) and index Pt. I. Basic theory. 1. Introduction. 1.1. Functional notation -- 2. Existence and uniqueness of smooth solutions. 2.1. The linear convection-diffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2 -- 3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3 -- 4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4 -- 5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5 -- 6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6 -- - A. Some theorems from functional analysis. A.1. The Calderón-Zygmund theorem. A.2. Young's and the Hardy-Littlewood-Sobolev inequalities. A.3. The Riesz-Thorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel -- pt. II. Approximate solutions. 7. Introduction -- 8. Notation. 8.1. One-dimensional discrete setting. 8.2. Two-dimensional discrete setting -- 9. Finite difference approximation to second-order boundary-value problems. 9.1. The principle of finite difference schemes. 9.2. The three-point Laplacian. 9.3. Matrix representation of the three-point Laplacian. 9.4. Notes for chapter 9 -- - 10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The three-point biharmonic operator. 10.4. Accuracy of the three-point biharmonic operator. 10.5. Coercivity and stability properties of the three-point biharmonic operator. 10.6. Matrix representation of the three-point biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10 -- 11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11 -- 12. Compact approximation of the Navier-Stokes equations in streamfunction formulation. 12.1. The Navier-Stokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12 -- - B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation -- 13. Fully discrete approximation of the Navier-Stokes equations. 13.1. Fourth-order approximation in space. 13.2. A time-stepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13 -- 14. Numerical simulations of the driven cavity problem. 14.1. Second-order scheme for the driven cavity problem. 14.2. Fourth-order scheme for the driven cavity problem. 14.3. Double-driven cavity problem. 14.4. Notes for chapter 14 This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "double-driven cavity". A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics SCIENCE / Mechanics / Fluids bisacsh Navier-Stokes equations fast Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Numerische Strömungssimulation (DE-588)4690080-9 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s Numerische Strömungssimulation (DE-588)4690080-9 s 1\p DE-604 Croisille, Jean-Pierre Sonstige oth Fishelov, Dalia Sonstige oth World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592580 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ben-Artzi, Matania Navier-Stokes equations in planar domains SCIENCE / Mechanics / Fluids bisacsh Navier-Stokes equations fast Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| subject_GND | (DE-588)4041456-5 (DE-588)4690080-9 |
| title | Navier-Stokes equations in planar domains |
| title_auth | Navier-Stokes equations in planar domains |
| title_exact_search | Navier-Stokes equations in planar domains |
| title_full | Navier-Stokes equations in planar domains Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov |
| title_fullStr | Navier-Stokes equations in planar domains Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov |
| title_full_unstemmed | Navier-Stokes equations in planar domains Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov |
| title_short | Navier-Stokes equations in planar domains |
| title_sort | navier stokes equations in planar domains |
| topic | SCIENCE / Mechanics / Fluids bisacsh Navier-Stokes equations fast Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| topic_facet | SCIENCE / Mechanics / Fluids Navier-Stokes equations Navier-Stokes-Gleichung Numerische Strömungssimulation |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=592580 |
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