Page 6 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Contents

Preface Xi

1. INTRODUCTION TO MECHANICS OF CONTINUA

1 Kinematics of Continua
1.1 The Concept of a Deformable Continuum
1.2 Motion of a Continuum.
Lagrangian and Eulerian Coordinates

13 Euler—Lagrange Criterion.
Euler’s and Reynolds’ (Transport) Theorems 13
General Principles.
The Stress Tensor and Cauchy’s Fundamental Results 17
2.1 The Forces Acting on a Continuum 17

2.2 Principle of Mass Conservation.
The Continuity Equation 18
2.3 Principle of the Momentum Torsor Variation.
The Balance Equations 20
2.4 The Cauchy Stress Tensor 21

2.5 The Cauchy Motion Equations 23
2.6 Principle of Energy Variation.
Conservation of Energy 24
2.7 General Conservation Principle 25

Constitutive Laws.
Inviscid and real fluids 26
3.1 Introductory Notions of Thermodynamics.
First and Second Law of Thermodynamics 26
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3.2 Constitutive (Behaviour, “Stresses-Deformations’
Relations) Laws 32
3.3 Inviscid (Ideal) Fluids 34

3.4 Real Fluids 38