Navier-Stokes equations in planar domains /:
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 pr...
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| Zusammenfassung: | 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 resource (xii, 302 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 287-297) and index. |
| ISBN: | 9781848162761 1848162766 |
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| 245 | 1 | 0 | |a Navier-Stokes equations in planar domains / |c Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov. |
| 260 | |a London : |b Imperial College Press ; |a Singapore : |b Distributed by World Scientific Pub. Co., |c ©2013. | ||
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| 504 | |a Includes bibliographical references (pages 287-297) and index. | ||
| 505 | 0 | |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 -- 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. | |
| 520 | |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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| contents | 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. |
| ctrlnum | (OCoLC)844311053 |
| 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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Co.,</subfield><subfield code="c">©2013.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xii, 302 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 287-297) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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 -- 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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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. 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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:21Z |
| institution | BVB |
| institution_GND | http://id.loc.gov/authorities/names/no2001005546 |
| isbn | 9781848162761 1848162766 |
| language | English |
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| spelling | Ben-Artzi, Matania, 1948- https://id.oclc.org/worldcat/entity/E39PCjHwrMbrg8qkcfdTMMGd73 http://id.loc.gov/authorities/names/n85275158 Navier-Stokes equations in planar domains / Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov. London : Imperial College Press ; Singapore : Distributed by World Scientific Pub. Co., ©2013. 1 online resource (xii, 302 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 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. Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Équations de Navier-Stokes. SCIENCE Mechanics Fluids. bisacsh Navier-Stokes equations fast Croisille, Jean-Pierre, 1961- https://id.oclc.org/worldcat/entity/E39PBJc7X6jF8jTmjcrDj44H4q http://id.loc.gov/authorities/names/n99256576 Fishelov, Dalia. World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 has work: Navier-Stokes equations in planar domains (Text) https://id.oclc.org/worldcat/entity/E39PCFHDHqkB74crBDKhTFwmbd https://id.oclc.org/worldcat/ontology/hasWork Print version: en-Artzi, Matania, 1948- Navier-Stokes equations in planar domains. London ; Hackensack, NJ : Imperial College Press, ©2013 9781848162754 (DLC) 2013427793 (OCoLC)824183287 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=592580 Volltext |
| spellingShingle | Ben-Artzi, Matania, 1948- Navier-Stokes equations in planar domains / 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. Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Équations de Navier-Stokes. SCIENCE Mechanics Fluids. bisacsh Navier-Stokes equations fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85090420 |
| 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 | Navier-Stokes equations. http://id.loc.gov/authorities/subjects/sh85090420 Équations de Navier-Stokes. SCIENCE Mechanics Fluids. bisacsh Navier-Stokes equations fast |
| topic_facet | Navier-Stokes equations. Équations de Navier-Stokes. SCIENCE Mechanics Fluids. Navier-Stokes equations |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=592580 |
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