Incompressible Flow and the Finite Element Method, 2 Volume Set

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.

Spis treści:
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 S tokes 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