{"product_id":"incompressible-flow-and-the-finite-element-method-volume-1-isbn-9780471492498","title":"Incompressible Flow and the Finite Element Method, Volume 1","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) \u003cp\u003e\u003cb\u003eVolume 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eGlossary of Abbreviations xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Incompressible Flow 3\u003c\/p\u003e \u003cp\u003e1.3 The Finite Element Method 6\u003c\/p\u003e \u003cp\u003e1.4 Incompressible Flow and the Finite Element Method 11\u003c\/p\u003e \u003cp\u003e1.5 Overview of this Volume 12\u003c\/p\u003e \u003cp\u003e1.6 Some Subjective Discussion 16\u003c\/p\u003e \u003cp\u003e1.7 Why Finite Elements? Why Not Finite Volumes? 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Advection-Diffusion Equation 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Continuum Equation 21\u003c\/p\u003e \u003cp\u003e2.2 The Finite Element Equations\/Discretization of the Weak Form 35\u003c\/p\u003e \u003cp\u003e2.3 Same Semi-Discrete Equations 56\u003c\/p\u003e \u003cp\u003e2.4 Open Boundary Conditions (OBC’s) 91\u003c\/p\u003e \u003cp\u003e2.5 Same Non-Galerkin Results 105\u003c\/p\u003e \u003cp\u003e2.6 Dispersion, Dissipation, Phase Speed, Group\u003c\/p\u003e \u003cp\u003e2.7 Time Integration 230\u003c\/p\u003e \u003cp\u003e2.8 Additional Numerical Examples 342\u003c\/p\u003e \u003cp\u003eAppendix 1 Some Element Matrices 357\u003c\/p\u003e \u003cp\u003eAppendix 2 Further Comparison of Finite Elements and Finite Volumes 365\u003c\/p\u003e \u003cp\u003eAppendix 3 Scalar Projections, Orthogonal and Not—and Projection Methods 379\u003c\/p\u003e \u003cp\u003eReferences 423\u003c\/p\u003e \u003cp\u003eAuthor Index Ai-1\u003c\/p\u003e \u003cp\u003eSubject Index Si-1\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVolume 2\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGlossary of Abbreviations xv\u003c\/p\u003e \u003cp\u003ePreface and Introduction xvii\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eIntroduction xx\u003c\/p\u003e \u003cp\u003eIncompressible Flow xxii\u003c\/p\u003e \u003cp\u003eThe Finite Element Method xxv\u003c\/p\u003e \u003cp\u003eIncompressible Flow and the Finite Element Method xxvi\u003c\/p\u003e \u003cp\u003eOverview of this Volume xxxi\u003c\/p\u003e \u003cp\u003eSome Subjective Discussion xxxv\u003c\/p\u003e \u003cp\u003eWhy Finite Elements? Why Not Finite Volumes? xxxvi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Navier–Stokes Equations 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Notational Introduction 447\u003c\/p\u003e \u003cp\u003e3.2 The Continuum Equations (The PDE’s) 450\u003c\/p\u003e \u003cp\u003e3.3 Alternate Forms of the Viscous Term 452\u003c\/p\u003e \u003cp\u003e3.4 Alternate Forms of the Non-Linear Term 454\u003c\/p\u003e \u003cp\u003e3.5 Derived Equations 457\u003c\/p\u003e \u003cp\u003e3.6 Alternate Statements of the NS Equations 461\u003c\/p\u003e \u003cp\u003e3.7 Special Cases of Interest 463\u003c\/p\u003e \u003cp\u003e3.8 Boundary Conditions 470\u003c\/p\u003e \u003cp\u003e3.9 Initial Conditions (and Well-Posedness) 487\u003c\/p\u003e \u003cp\u003e3.10 Interim Summary 493\u003c\/p\u003e \u003cp\u003e3.11 Global Conservation Laws 502\u003c\/p\u003e \u003cp\u003e3.12 Weak Forms of the PDE’s\/Natural Boundary Conditions (NBC’s) 508\u003c\/p\u003e \u003cp\u003e3.13 The Finite Element Equations\/Discretization of the Weak Form 528\u003c\/p\u003e \u003cp\u003e3.14 A Control Volume Finite Element Method 712\u003c\/p\u003e \u003cp\u003e3.15 Variational Principles for Potential and Stokes Flow 716\u003c\/p\u003e \u003cp\u003e3.16 Solution Methods for the Semi-Discretized Time-Dependent (and Steady) Equations 729\u003c\/p\u003e \u003cp\u003e3.17 Aliasing and Aliasing Instability, Linear and Non-Linear 876\u003c\/p\u003e \u003cp\u003e3.18 A New Look al Two Old Finite Difference Methods 880\u003c\/p\u003e \u003cp\u003e3.19 Numerical Example-Impulsive Start 884\u003c\/p\u003e \u003cp\u003e3.20 Closure: Some Additional Remarks on the Pressure 934\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Derived Quantities 937\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 937\u003c\/p\u003e \u003cp\u003e4.2 Two Dimensions 938\u003c\/p\u003e \u003cp\u003e4.3 Three Dimensions 961\u003c\/p\u003e \u003cp\u003e4.3.1 Vorticity 961\u003c\/p\u003e \u003cp\u003e4.3.2 Helicity Density 961\u003c\/p\u003e \u003cp\u003eAppendix 4 Some More Element Matrices 963\u003c\/p\u003e \u003cp\u003eAppendix 5 Vector Projections, Orthogonal and Not—and Projection Methods 967\u003c\/p\u003e \u003cp\u003eReferences 989\u003c\/p\u003e \u003cp\u003eAuthor Index Ai-1\u003c\/p\u003e \u003cp\u003eSubject Index Si-1\u003c\/p\u003e  \u003cp\u003eP. M. Gresho is the author of Incompressible Flow and the Finite Element Method, Volume 1: Advection-Diffusion and Isothermal Laminar Flow, published by Wiley. R. L. Sani is the author of Incompressible Flow and the Finite Element Method, Volume 1: Advection-Diffusion and 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 * consistent pressure Poisson equation\u003cbr\u003e * consistent penalty methods\u003cbr\u003e * consistent normal direction\u003cbr\u003e * consistent heat flux\u003cbr\u003e * consistent forces\u003cbr\u003e Fully indexed and referenced\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989413970149,"sku":"NP9780471492498","price":174.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471492498.jpg?v=1761784010","url":"https:\/\/k12savings.com\/products\/incompressible-flow-and-the-finite-element-method-volume-1-isbn-9780471492498","provider":"K12savings","version":"1.0","type":"link"}