Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

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Springer Science & Business Media, Jun 14, 2006 - Mathematics - 500 pages
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The present book – through the topics and the problems approach – aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics). Our presentation results from a large documentation and focuses on reviewing the present day most important numerical and computational methods in CFD. Many theoreticians and experts in the field have expressed their - terest in and need for such an enterprise. This was the motivation for carrying out our study and writing this book. It contains an important systematic collection of numerical working instruments in Fluid Dyn- ics. Our current approach to CFD started ten years ago when the Univ- sity of Paris XI suggested a collaboration in the field of spectral methods for fluid dynamics. Soon after – preeminently studying the numerical approaches to Navier–Stokes nonlinearities – we completed a number of research projects which we presented at the most important inter- tional conferences in the field, to gratifying appreciation. An important qualitative step in our work was provided by the dev- opment of a computational basis and by access to a number of expert softwares. This fact allowed us to generate effective working programs for most of the problems and examples presented in the book, an - pect which was not taken into account in most similar studies that have already appeared all over the world.
 

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Contents

Kinematics of Continua
1
General Principles
16
Constitutive Laws
26
vi
43
Shock Waves
49
x
68
5
79
Almost Potential Fluid Flow
92
INTRODUCTION TO NUMERICAL SOLUTIONS
196
FINITEDIFFERENCE METHODS
247
Elliptic Equations
295
FINITE ELEMENT AND BOUNDARY ELEMENT
345
LeastSquares Finite Element Method LSFEM
356
THE FINITE VOLUME METHOD
397
SPECTRAL METHODS
439
Appendix
483

Unsteady Irrotational Flows Generated by the Motion
100
VISCOUS INCOMPRESSIBLE FLUID DYNAMICS
133
viii
157

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