Turbulence is the most fundamental and, simultaneously, the most complex form of fluid flow. However, because an understanding of turbulence requires an understanding of laminar flow, both are explored in this book. Groundwork is laid by careful delineation of the necessary physical, mathematical, and numerical requirements for the studies which follow, and include discussions of N-body problems, classical molecular mechanics, dynamical equations, and the leap frog formulas for very large systems of second order ordinary differential equations. Molecular systems are studied first in both two and three dimensions. Extension into the large is also of great interest, and it is for this purpose that we develop particle mechanics, which uses lump massing of molecules. All calculations are limited to a personal scientific computer, so that the methods can be utilized readily by others.
Author(s): Donald Greenspan
Publisher: World Scientific Pub Co Inc
Year: 2005
Language: English
Pages: 180
Tags: Механика;Механика жидкостей и газов;Турбулентность;
Preface......Page 6
Contents......Page 8
1.2. Classical Molecular Potentials......Page 12
1.4. The Leap Frog Formulas......Page 15
1.5. Turbulence......Page 19
1.5.2. Theoretical......Page 20
1.6. Overview......Page 21
2.1. Introduction......Page 24
2.2. Equations of Motion for Argon Vapor......Page 25
2.3. The Cavity Problem......Page 26
2.4. Computational Considerations......Page 27
2.5. Examples of Primary Vortex Generation......Page 28
2.6. Example of Turbulent Flow......Page 33
2.8. The Fortran Program ARGON.FOR......Page 40
2.9. The Fortran Program YOUWIN.FOR......Page 43
3.1. Molecular Formulas......Page 48
3.3. Initial Data......Page 49
3.4. Examples of Primary Vortex Generation......Page 50
3.5. Turbulent Flow......Page 55
3.6. The Fortran Program AIR.FOR......Page 62
4.2. Equations of Motion for Water Vapor Molecules......Page 66
4.3. Examples of Primary Vortex Generation......Page 68
4.4. Example of Turbulent Flow......Page 71
4.5. A Speculative Study of Liquid Water......Page 76
4.6. The Fortran Program CAV.FOR......Page 81
5.1. Introduction......Page 86
5.2. Molecular Arrangement and the Cavity Problem......Page 87
5.4. Examples......Page 89
5.5. Turbulent Flow......Page 98
5.6. The Fortran program CAV3D.FOR......Page 106
6.2. Particle Arrangement and Equations......Page 110
6.4. Examples......Page 114
6.5. Turbulence......Page 119
6.6. Heating Water Vapor in a Square Cavity......Page 123
6.7. A Speculative Study of Liquid Water......Page 127
6.8. Particle Equations of Motion......Page 129
6.9. Particle Equilibrium......Page 132
6.10. Primary Vortex Generation......Page 133
6.11. Turbulence......Page 140
6.12. The Fortran Program PARTICLE.FOR......Page 144
7.2. Mathematical and Physical Preliminaries......Page 148
7.3. Approximate Equations......Page 149
7.4. Problem Formulation......Page 150
7.5. Examples......Page 152
7.6. Remarks......Page 161
7.7. The Fortran Program PLATE.FOR......Page 163
8.2. Concepts of Infinity......Page 166
8.3. The Surface Area Paradox......Page 168
8.4. Paradoxes of Zeno......Page 170
8.5. A Nonsolvable Problem in Population Genetics......Page 171
8.7. Remark......Page 172
References and Additional Sources......Page 174
Index......Page 178
