{"product_id":"incompressible-flow-and-the-finite-element-method-volume-2-isbn-9780471492504","title":"Incompressible Flow and the Finite Element Method, Volume 2","description":"This comprehensive two-volume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution.\u003cbr\u003e \u003cbr\u003e Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes equations (covered in detail in Volume Two) - a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained.\u003cbr\u003e \u003cbr\u003e The book explains and emphasizes consistency in six areas:\u003cbr\u003e \u003cbr\u003e * consistent mass matrix\u003cbr\u003e \u003cbr\u003e * consistent pressure Poisson equation\u003cbr\u003e \u003cbr\u003e * consistent penalty methods\u003cbr\u003e \u003cbr\u003e * consistent normal direction\u003cbr\u003e \u003cbr\u003e * consistent heat flux\u003cbr\u003e \u003cbr\u003e * consistent forces\u003cbr\u003e \u003cbr\u003e Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.Das umfangreiche Handbuch zur Anwendung finiter Elemente auf die inkompressible Strömung: Jetzt neu als preiswerte Paperback-Ausgabe! Ausgehend von einer ausführlichen Erläuterung der theoretischen Grundlagen werden geeignete numerische Methoden zur Lösung vielfältiger Strömungsprobleme abgeleitet. Die in der Praxis außerordentlich wichtigen Anfangs- und Randbedingungen werden besonders sorgfältig behandelt. Nicht zuletzt finden sich Angaben zur bisher oft kontrovers diskutierten Rolle des Druckes. (06\/00)  Glossary of Abbreviations\u003cbr\u003e Preface and Introduction\u003cbr\u003e 3. The Navier-Stokes Equations\u003cbr\u003e 3.1 Notational Introduction\u003cbr\u003e 3.2 The Continuum Equations\u003cbr\u003e 3.3 Alternate Forms of the Viscous Term\u003cbr\u003e 3.4 Alternate Forms of the Non-Linear Term\u003cbr\u003e 3.5 Derived Equations\u003cbr\u003e 3.6 Alternate Statements of the NS Equations\u003cbr\u003e 3.7 Special Cases of Interest\u003cbr\u003e 3.8 Boundary Conditions\u003cbr\u003e 3.9 Initial Conditions (and Well-Posedness)\u003cbr\u003e 3.10 Interim Summary\u003cbr\u003e 3.11 Global Conservation Laws\u003cbr\u003e 3.12 Weak Form of the PDE's \/\u003cbr\u003e Natural Boundary Conditions (NBC's)\u003cbr\u003e 3.13 The Finite Element Equations \/\u003cbr\u003e Discretization of the Weak Form\u003cbr\u003e 3.14 A Control Volume Finite Element Method\u003cbr\u003e 3.15 Variational Principles for Potential and Stokes Flow\u003cbr\u003e 3.16 Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations\u003cbr\u003e 3.17 Aliasing and Aliasing Instability, Linear and Non-Linear\u003cbr\u003e 3.18 A New Look at Two Old Finite Difference Methods\u003cbr\u003e 3.19 Numerical Example -\u003cbr\u003e Implusive Start\u003cbr\u003e 3.20 Closure: Some Additional Remarks on the Pressure\u003cbr\u003e 4. Derived Quantities\u003cbr\u003e 4.1 Introduction\u003cbr\u003e 4.2 Two Dimensions\u003cbr\u003e 4.3 Three Dimensions\u003cbr\u003e Appendix 1 Some Element Matrix\u003cbr\u003e A.1.1 Advection Diffusion Matrices\u003cbr\u003e A.1.2 One-Dimensional Element Matrices\u003cbr\u003e A.1.3 Two-Dimensional Element Matrices\u003cbr\u003e A.1.4 Navier-Stokes: Additional Matrices\u003cbr\u003e A.1.5 Two-Dimensional Control Volume Finite Element Matrices\u003cbr\u003e Appendix 2 Further Comparison of Finite Elements and Finite\u003cbr\u003e Volumes\u003cbr\u003e A.2.1 Introduction\u003cbr\u003e A.2.2 Viewpoint One\u003cbr\u003e A.2.3 Viewpoint Two\u003cbr\u003e Appendix 3 Projections, Orthagonal and Not and Projection Methods\u003cbr\u003e A.3.1 Introduction\u003cbr\u003e A.3.2 Scalar Projections\u003cbr\u003e A.3.3 Vector Projections\u003cbr\u003e References\u003cbr\u003e Author Index\u003cbr\u003e Subject Index  \u003cp\u003eP. M. Gresho is the author of Incompressible Flow and the Finite Element Method, Volume 2: Isothermal Laminar Flow, published by Wiley. R. L. Sani is the author of Incompressible Flow and the Finite Element Method, Volume 2: Isothermal Laminar Flow, published by Wiley.   This comprehensive two volume reference work is devoted to the important details regarding the application of the finite element method to incompressible flows, addressing the theoretical background and the detailed development of appropriate numerical methods applied to their solution. Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. In addition, for both this equation and the equations of principal interest - the Navier-Stokes equations - (covered in detail in Volume Two), a discussion of both the continuous and discrete equations is presented. Also addressed are explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are thoroughly described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained. Together, this two volume work explains and emphasizes consistency in six areas:\u003cbr\u003e * consistent mass matrix\u003cbr\u003e \u003cbr\u003e * consistent pressure Poisson equation\u003cbr\u003e \u003cbr\u003e * consistent penalty methods\u003cbr\u003e \u003cbr\u003e * consistent normal direction\u003cbr\u003e \u003cbr\u003e * consistent heat flux\u003cbr\u003e \u003cbr\u003e * consistent forces\u003cbr\u003e Fully indexed and referenced, these two volumes form an essential reference tool for all research students and applied scientists in incompressible fluid mechanics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989413937381,"sku":"NP9780471492504","price":209.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471492504.jpg?v=1761784010","url":"https:\/\/k12savings.com\/es\/products\/incompressible-flow-and-the-finite-element-method-volume-2-isbn-9780471492504","provider":"K12savings","version":"1.0","type":"link"}