Basic control volume finite element methods for fluids and solids /:
The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ : Bangalore (India) :
World Scientific ; IISc Press,
©2009.
|
| Schriftenreihe: | IISc research monographs series ;
v. 1. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems. |
| Beschreibung: | 1 online resource (xiv, 170 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 167-168) and index. |
| ISBN: | 9789812834997 9812834990 |
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| 245 | 1 | 0 | |a Basic control volume finite element methods for fluids and solids / |c Vaughan R. Voller. |
| 260 | |a Hackensack, NJ : |b World Scientific ; |a Bangalore (India) : |b IISc Press, |c ©2009. | ||
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| 505 | 0 | |a 1. Introduction. 1.1. Overview. 1.2. Objective and philosophy. 1.3. The basic control volume concept. 1.4. Main topics covered -- 2. Governing equations. 2.1. The Euler equations of motion. 2.2. Specific governing equations -- 3. The essential ingredients in a numerical solution. 3.1. The basic idea. 3.2. The discretization : grid, mesh, and cloud. 3.3. The element and the interpolation shape functions. 3.4. Region of support and control volume. 3.5. The discrete equation -- 4. Control volume finite element data structure. 4.1. The task. 4.2. The mesh. 4.3. The data structure. 4.4. The discrete equation. 4.5. Summary -- 5. Control volume finite element method (CVFEM) discretization and solution. 5.1. The approach. 5.2. Preliminary calculations. 5.3. Steady state diffusion. 5.4. Steady state advection-diffusion. 5.5. Steady state advection-diffusion with source terms. 5.6. Coding issues. 5.7. Boundary conditions. 5.8. Solution. 5.9. Handling variable diffusivity. 5.10. Transients. 5.11. Summary -- 6. The control volume finite difference method. 6.1. The task. 6.2. CVFDM data structure. 6.3. Coefficients and sources. 6.4. Boundary conditions. 6.5. Summary -- 7. Analytical and CVFEM solutions of advection-diffusion equations. 7.1. The task. 7.2. Choice of test problems. 7.3. One-dimensional steady state diffusion in a finite domain. 7.4. One-dimensional transient diffusion in a semi-Infinited domain. 7.5. One-dimensional transient advection-diffusion in a semi-infinite domain. 7.6. Steady state diffusion in an annulus. 7.7. Steady state advection diffusion in an annulus. 7.8. Transient diffusion from a line source. 7.9. The recharge well problem -- 8. A plane stress CVFEM solution. 8.1. Introduction. 8.2. The stress concentration problem. 8.3. CVFEM displacement solution. 8.4. The stress solution. 8.5. Summary -- 9. CVFEM stream function-vorticity solution for a lid driven cavity flow. 9.1. Introduction. 9.2. The governing equations. 9.3. The CVFEM discretization of the stream function equation. 9.4. The CVFEM discretization of the vorticity equation. 9.5. Solution steps. 9.6. Results -- 10. Notes toward the development of a 3-D CVFEM code. 10.1. The tetrahedron element. 10.2. Creating a mesh of tetrahedron elements. 10.3. Geometric features of tetrahedrons. 10.4. Volume shape functions. 10.5. The control volume and face. 10.6. Approximation of face fluxes. 10.7. Summary. | |
| 520 | |a The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems. | ||
| 650 | 0 | |a Finite element method. |0 http://id.loc.gov/authorities/subjects/sh85048349 | |
| 650 | 0 | |a Finite volume method. |0 http://id.loc.gov/authorities/subjects/sh95001595 | |
| 650 | 6 | |a Méthode des éléments finis. | |
| 650 | 6 | |a Méthodes de volumes finis. | |
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| 776 | 0 | 8 | |i Print version: |a Voller, V.R. (Vaughan R.). |t Basic control volume finite element methods for fluids and solids. |d Hackensack, NJ : World Scientific ; Banaglore? : IISc Press, ©2009 |z 9789812834980 |w (DLC) 2009277983 |w (OCoLC)519740608 |
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| author | Voller, V. R. (Vaughan R.) |
| author_GND | http://id.loc.gov/authorities/names/n94109533 |
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| contents | 1. Introduction. 1.1. Overview. 1.2. Objective and philosophy. 1.3. The basic control volume concept. 1.4. Main topics covered -- 2. Governing equations. 2.1. The Euler equations of motion. 2.2. Specific governing equations -- 3. The essential ingredients in a numerical solution. 3.1. The basic idea. 3.2. The discretization : grid, mesh, and cloud. 3.3. The element and the interpolation shape functions. 3.4. Region of support and control volume. 3.5. The discrete equation -- 4. Control volume finite element data structure. 4.1. The task. 4.2. The mesh. 4.3. The data structure. 4.4. The discrete equation. 4.5. Summary -- 5. Control volume finite element method (CVFEM) discretization and solution. 5.1. The approach. 5.2. Preliminary calculations. 5.3. Steady state diffusion. 5.4. Steady state advection-diffusion. 5.5. Steady state advection-diffusion with source terms. 5.6. Coding issues. 5.7. Boundary conditions. 5.8. Solution. 5.9. Handling variable diffusivity. 5.10. Transients. 5.11. Summary -- 6. The control volume finite difference method. 6.1. The task. 6.2. CVFDM data structure. 6.3. Coefficients and sources. 6.4. Boundary conditions. 6.5. Summary -- 7. Analytical and CVFEM solutions of advection-diffusion equations. 7.1. The task. 7.2. Choice of test problems. 7.3. One-dimensional steady state diffusion in a finite domain. 7.4. One-dimensional transient diffusion in a semi-Infinited domain. 7.5. One-dimensional transient advection-diffusion in a semi-infinite domain. 7.6. Steady state diffusion in an annulus. 7.7. Steady state advection diffusion in an annulus. 7.8. Transient diffusion from a line source. 7.9. The recharge well problem -- 8. A plane stress CVFEM solution. 8.1. Introduction. 8.2. The stress concentration problem. 8.3. CVFEM displacement solution. 8.4. The stress solution. 8.5. Summary -- 9. CVFEM stream function-vorticity solution for a lid driven cavity flow. 9.1. Introduction. 9.2. The governing equations. 9.3. The CVFEM discretization of the stream function equation. 9.4. The CVFEM discretization of the vorticity equation. 9.5. Solution steps. 9.6. Results -- 10. Notes toward the development of a 3-D CVFEM code. 10.1. The tetrahedron element. 10.2. Creating a mesh of tetrahedron elements. 10.3. Geometric features of tetrahedrons. 10.4. Volume shape functions. 10.5. The control volume and face. 10.6. Approximation of face fluxes. 10.7. Summary. |
| ctrlnum | (OCoLC)568540094 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:17:02Z |
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| series | IISc research monographs series ; |
| series2 | IISc research monograph series ; |
| spelling | Voller, V. R. (Vaughan R.) https://id.oclc.org/worldcat/entity/E39PCjtWqWkxVkJG6y8CKkcRqP http://id.loc.gov/authorities/names/n94109533 Basic control volume finite element methods for fluids and solids / Vaughan R. Voller. Hackensack, NJ : World Scientific ; Bangalore (India) : IISc Press, ©2009. 1 online resource (xiv, 170 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier IISc research monograph series ; v. 1 Includes bibliographical references (pages 167-168) and index. Print version record. 1. Introduction. 1.1. Overview. 1.2. Objective and philosophy. 1.3. The basic control volume concept. 1.4. Main topics covered -- 2. Governing equations. 2.1. The Euler equations of motion. 2.2. Specific governing equations -- 3. The essential ingredients in a numerical solution. 3.1. The basic idea. 3.2. The discretization : grid, mesh, and cloud. 3.3. The element and the interpolation shape functions. 3.4. Region of support and control volume. 3.5. The discrete equation -- 4. Control volume finite element data structure. 4.1. The task. 4.2. The mesh. 4.3. The data structure. 4.4. The discrete equation. 4.5. Summary -- 5. Control volume finite element method (CVFEM) discretization and solution. 5.1. The approach. 5.2. Preliminary calculations. 5.3. Steady state diffusion. 5.4. Steady state advection-diffusion. 5.5. Steady state advection-diffusion with source terms. 5.6. Coding issues. 5.7. Boundary conditions. 5.8. Solution. 5.9. Handling variable diffusivity. 5.10. Transients. 5.11. Summary -- 6. The control volume finite difference method. 6.1. The task. 6.2. CVFDM data structure. 6.3. Coefficients and sources. 6.4. Boundary conditions. 6.5. Summary -- 7. Analytical and CVFEM solutions of advection-diffusion equations. 7.1. The task. 7.2. Choice of test problems. 7.3. One-dimensional steady state diffusion in a finite domain. 7.4. One-dimensional transient diffusion in a semi-Infinited domain. 7.5. One-dimensional transient advection-diffusion in a semi-infinite domain. 7.6. Steady state diffusion in an annulus. 7.7. Steady state advection diffusion in an annulus. 7.8. Transient diffusion from a line source. 7.9. The recharge well problem -- 8. A plane stress CVFEM solution. 8.1. Introduction. 8.2. The stress concentration problem. 8.3. CVFEM displacement solution. 8.4. The stress solution. 8.5. Summary -- 9. CVFEM stream function-vorticity solution for a lid driven cavity flow. 9.1. Introduction. 9.2. The governing equations. 9.3. The CVFEM discretization of the stream function equation. 9.4. The CVFEM discretization of the vorticity equation. 9.5. Solution steps. 9.6. Results -- 10. Notes toward the development of a 3-D CVFEM code. 10.1. The tetrahedron element. 10.2. Creating a mesh of tetrahedron elements. 10.3. Geometric features of tetrahedrons. 10.4. Volume shape functions. 10.5. The control volume and face. 10.6. Approximation of face fluxes. 10.7. Summary. The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Méthode des éléments finis. Méthodes de volumes finis. MATHEMATICS Numerical Analysis. bisacsh Finite element method fast Finite volume method fast has work: Basic control volume finite element methods for fluids and solids (Text) https://id.oclc.org/worldcat/entity/E39PCFX8TpFbTrhP3XCbXwTBrq https://id.oclc.org/worldcat/ontology/hasWork Print version: Voller, V.R. (Vaughan R.). Basic control volume finite element methods for fluids and solids. Hackensack, NJ : World Scientific ; Banaglore? : IISc Press, ©2009 9789812834980 (DLC) 2009277983 (OCoLC)519740608 IISc research monographs series ; v. 1. http://id.loc.gov/authorities/names/no2009096980 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305233 Volltext |
| spellingShingle | Voller, V. R. (Vaughan R.) Basic control volume finite element methods for fluids and solids / IISc research monographs series ; 1. Introduction. 1.1. Overview. 1.2. Objective and philosophy. 1.3. The basic control volume concept. 1.4. Main topics covered -- 2. Governing equations. 2.1. The Euler equations of motion. 2.2. Specific governing equations -- 3. The essential ingredients in a numerical solution. 3.1. The basic idea. 3.2. The discretization : grid, mesh, and cloud. 3.3. The element and the interpolation shape functions. 3.4. Region of support and control volume. 3.5. The discrete equation -- 4. Control volume finite element data structure. 4.1. The task. 4.2. The mesh. 4.3. The data structure. 4.4. The discrete equation. 4.5. Summary -- 5. Control volume finite element method (CVFEM) discretization and solution. 5.1. The approach. 5.2. Preliminary calculations. 5.3. Steady state diffusion. 5.4. Steady state advection-diffusion. 5.5. Steady state advection-diffusion with source terms. 5.6. Coding issues. 5.7. Boundary conditions. 5.8. Solution. 5.9. Handling variable diffusivity. 5.10. Transients. 5.11. Summary -- 6. The control volume finite difference method. 6.1. The task. 6.2. CVFDM data structure. 6.3. Coefficients and sources. 6.4. Boundary conditions. 6.5. Summary -- 7. Analytical and CVFEM solutions of advection-diffusion equations. 7.1. The task. 7.2. Choice of test problems. 7.3. One-dimensional steady state diffusion in a finite domain. 7.4. One-dimensional transient diffusion in a semi-Infinited domain. 7.5. One-dimensional transient advection-diffusion in a semi-infinite domain. 7.6. Steady state diffusion in an annulus. 7.7. Steady state advection diffusion in an annulus. 7.8. Transient diffusion from a line source. 7.9. The recharge well problem -- 8. A plane stress CVFEM solution. 8.1. Introduction. 8.2. The stress concentration problem. 8.3. CVFEM displacement solution. 8.4. The stress solution. 8.5. Summary -- 9. CVFEM stream function-vorticity solution for a lid driven cavity flow. 9.1. Introduction. 9.2. The governing equations. 9.3. The CVFEM discretization of the stream function equation. 9.4. The CVFEM discretization of the vorticity equation. 9.5. Solution steps. 9.6. Results -- 10. Notes toward the development of a 3-D CVFEM code. 10.1. The tetrahedron element. 10.2. Creating a mesh of tetrahedron elements. 10.3. Geometric features of tetrahedrons. 10.4. Volume shape functions. 10.5. The control volume and face. 10.6. Approximation of face fluxes. 10.7. Summary. Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Méthode des éléments finis. Méthodes de volumes finis. MATHEMATICS Numerical Analysis. bisacsh Finite element method fast Finite volume method fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048349 http://id.loc.gov/authorities/subjects/sh95001595 |
| title | Basic control volume finite element methods for fluids and solids / |
| title_auth | Basic control volume finite element methods for fluids and solids / |
| title_exact_search | Basic control volume finite element methods for fluids and solids / |
| title_full | Basic control volume finite element methods for fluids and solids / Vaughan R. Voller. |
| title_fullStr | Basic control volume finite element methods for fluids and solids / Vaughan R. Voller. |
| title_full_unstemmed | Basic control volume finite element methods for fluids and solids / Vaughan R. Voller. |
| title_short | Basic control volume finite element methods for fluids and solids / |
| title_sort | basic control volume finite element methods for fluids and solids |
| topic | Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Finite volume method. http://id.loc.gov/authorities/subjects/sh95001595 Méthode des éléments finis. Méthodes de volumes finis. MATHEMATICS Numerical Analysis. bisacsh Finite element method fast Finite volume method fast |
| topic_facet | Finite element method. Finite volume method. Méthode des éléments finis. Méthodes de volumes finis. MATHEMATICS Numerical Analysis. Finite element method Finite volume method |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305233 |
| work_keys_str_mv | AT vollervr basiccontrolvolumefiniteelementmethodsforfluidsandsolids |