Incompressible Flow and the Finite Element Method, 2 Volume Set

P. M. Gresho, R. L. Sani (Autoren)

Buch | Softcover

1112 Seiten

2000
John Wiley & Sons Inc (Verlag)
978-0-471-49268-9 (ISBN)

Titel z.Zt. nicht lieferbar
Versandkostenfrei
Auch auf Rechnung

Artikel merken

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.

P. M. Gresho is the author of Incompressible Flow and the Finite Element Method, 2 Volume Set, published by Wiley. R. L. Sani is the author of Incompressible Flow and the Finite Element Method, 2 Volume Set, published by Wiley.

1. Glossary of Abbreviations

2. Preface and Introduction

3. The Navier-Stokes Equations

Notational Introduction

The Continuum Equations

Alternate Forms of the Viscous Term

Alternate Forms of the Non-Linear Term

Derived Equations

Alternate Statements of the NS Equations

Special Cases of Interest

Boundary Conditions

Initial Conditions (and Well-Posedness)

Interim Summary

Global Conservation Laws

Weak Form of the PDEhod

Variational Principles for Potential and Stokes Flow

Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations

Aliasing and Aliasing Instability, Linear and Non-Linear

A New Look at Two Old Finite Difference Methods

Numerical Example

Closure: Some Additional Remarks on the Pressure

4. Derived Quantities

Introduction

Two Dimensions

Three Dimensions

Appendix 1 Some Element Matrix

Appendix 2 Further Comparison of Finite Elements and Finite Volumes

Appendix 3 Projections, Orthagonal and Not and Projection Methods

References

Author Index

Subject Index

Reihe/Serie	Incompressible Flow and the Finite Element Method \| 1.10
Verlagsort	New York
Sprache	englisch
Maße	178 x 246 mm
Gewicht	1724 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
Themenwelt	Technik ► Maschinenbau
ISBN-10	0-471-49268-X / 047149268X
ISBN-13	978-0-471-49268-9 / 9780471492689
Zustand	Neuware