Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

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Springer Science & Business Media, Dec 15, 2004 - 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

INTRODUCTION TO MECHANICS OF CONTINUA
1
VI
9
General Principles
16
Constitutive Laws
26
DYNAMICS OF INVISCID FLUIDS
51
Irrotational Flows of Incompressible Inviscid Fluids
59
Principles of the Wing Profiles Theory
70
Conformal Mapping
79
The Cauchy Problem for Ordinary Differential Equations
207
FINITEDIFFERENCE METHODS
247
Discretization of the Partial Differential Equations
253
Burgers Equation Without Shock
277
Elliptic Equations
295
Compact Finite Differences
320
Coordinate Transformation
335
FINITE ELEMENT AND BOUNDARY ELEMENT
345

Almost Potential Fluid Flow
92
Unsteady Irrotational Flows Generated by the Motion
100
Notions on the Steady Compressible Barotropic Flows
110
Mach Lines Weak Discontinuity Surfaces
123
VISCOUS INCOMPRESSIBLE FLUID DYNAMICS
133
Equivalent Formulations for the NavierStokes
140
Vlli
157
Plaque
191
INTRODUCTION TO NUMERICAL SOLUTIONS
197
LeastSquares Finite Element Method LSFEM
356
Boundary Element Method BEM
380
THE FINITE VOLUME METHOD
397
Generalized Difference Method
411
SPECTRAL METHODS
439
Appendix
483
Index
497
Copyright

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Page 495 - WATSON, GN A treatise on the theory of Bessel functions (Cambridge, 1922).
Page 488 - Cardos., Vladimir General integral method in the study of supersonic flows past slender bodies. Rev. Roum. Math. Pures Appl. 37. No.7, 571-577 (1992). 760.76039 Chakrabarti, A.; Vijayabharathi, L.

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