Incompressible Flow and the Finite Element Method: Volume 1: Advection-Diffusion, Volume 2: Isothermal Laminar Flow
Covers the applications of the finite element method to incompressible flows.
 |
 |
Format: Two Volume Set, Paperback, English, 1097 pages Other Versions: Volume 2, Paperback
|
Buy This Book From:
|
Have you read this book? Write your own Review
3 readers have reviewed this book. Average Rating: 
Publisher Comments
Now available as a two volume paperback…
This comprehensive reference work covers all the important details regarding the application of the finite element method to incompressible flows. It addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection-diffusion equation in volume one. For both this equation and the equations of principal interest - the Navier-Stokes equations, covered in detail in volume two - detailed 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.
Together, this two volume work explains and emphasizes consistency in six areas:
- consistent mass matrix
- consistent pressure Poisson equation
- consistent penalty methods
- consistent normal direction
- consistent heat flux
- consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
Reader Comments
incompressible flow and the finite element method
incompressibel flow and the finite element method
Incompressible Flow and the Finite Element Method
Table of Contents
| VOLUME ONE | ||
| Preface | ||
| Glossary of Abbreviations | ||
| 1. | Introduction | |
| 1.1 | Introduction | |
| 1.2 | Incompressible Flow | |
| 1.3 | The Finite Element Method | |
| 1.4 | Incompressible Flow and the Finite Element Method | |
| 1.5 | Overview of this Volume | |
| 1.6 | Some Subjective Discussion | |
| 1.7 | Why Finite Elements? Why Not Finite Volumes? | |
| 2. | The Advection-Diffusion Equation | |
| 2.1 | The Continuum Equation | |
| 2.2 | The Finite Element Equations / Discretization of the Weak Form | |
| 2.3 | Some Semi-Discrete Equations | |
| 2.4 | Open Boundary Conditions (OBC’s) | |
| 2.5 | Some Non-Galerkin Results | |
| 2.6 | Dispersion, Dissipation, Phase Speed, Group Velocity, Mesh Design, and – Wiggles | |
| 2.7 | Time Integration | |
| 2.8 | Additional Numerical Examples | |
| Appendix 1 | Some Element Matrices | |
| A.1.1 | Advection Diffusion Matrices | |
| A.1.2 | One-Dimensional Element Matrices | |
| A.1.3 | Two-Dimensional Element Matrices | |
| A.1.4 | Two Dimensional Control Volume Finite Element Matrices | |
| Appendix 2 | Further Comparison of Finite Elements and Finite Volumes | |
| A.2.1 | Introduction | |
| A.2.2 | Viewpoint One | |
| A.2.3 | Viewpoint Two | |
| Appendix 3 | Scalar Projections, Orthogonal and Not – and Projection Methods | |
| A.3.1 | Introduction | |
| A.3.2 | Scalar Projections | |
| References | ||
| Author Index | ||
| Subject Index | ||
| VOLUME TWO | ||
| Glossary of Abbreviations | ||
| Preface and Introduction | ||
| 3. | The Navier-Stokes Equations | |
| 3.1 | Notational Introduction | |
| 3.2 | The Continuum Equations | |
| 3.3 | Alternate Forms of the Viscous Term | |
| 3.4 | Alternate Forms of the Non-Linear Term | |
| 3.5 | Derived Equations | |
| 3.6 | Alternate Statements of the NS Equations | |
| 3.7 | Special Cases of Interest | |
| 3.8 | Boundary Conditions | |
| 3.9 | Initial Conditions (and Well-Posedness | |
| 3.10 | Interim Summary | |
| 3.11 | Global Conservation Laws | |
| 3.12 | Weak Form of the PDE’s / Natural Boundary Conditions (NBC’s) | |
| 3.13 | The Finite Element Equations / Discretization of the Weak Form | |
| 3.14 | A Control Volume Finite Element Method | |
| 3.15 | Variational Principles for Potential and Stokes Flow | |
| 3.16 | Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations | |
| 3.17 | Aliasing and Aliasing Instability, Linear and Non-Linear | |
| 3.18 | A New Look at Two Old Finite Difference Methods | |
| 3.19 | Numerical Example – Implusive Start | |
| 3.20 | Closure: Some Additional Remarks on the Pressure |
Related Book Categories
CFD for Incompressible Flows, Finite Element Methods
