文档介绍：BASICS OF FLUID MECHANICS AND
INTRODUCTION PUTATIONAL
FLUID DYNAMICS
by
TITUS PETRILA
Babes-Bolyai University, Cluj-Napoca, Romania
DAMIAN TRIF
Babes-Bolyai University, Cluj-Napoca, Romania
Springer
Library of Congress Cataloging-in-Publication Data
eBook ISBN: 0-387-23838-7
Print ISBN: 0-387-23837-9
©2005 Springer Science + Business Media, Inc.
Print ©2005 Springer Science + Business Media, Inc.
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Contents
Preface xiii
1. INTRODUCTION TO MECHANICS OF CONTINUA 1
1 Kinematics of Continua 1
The Concept of a Deformable Continuum 1
Motion of a Continuum.
Lagrangian and Eulerian Coordinates 4
Euler–Lagrange Criterion.
Euler’s and Reynolds’(Transport) Theorems 13
2 General Principles.
The Stress Tensor and Cauchy’s Fundamental Results 17
The Forces Acting on a Continuum 17
Principle of Mass Conservation.
The Continuity Equation 18
Principle of the Momentum Torsor Variation.
The Balance Equations 20
The Cauchy Stress Tensor 21
The Cauchy Motion Equations 23
Principle of Energy Variation.
Conservation of Energy 24
General Conservation Principle 25
3 Constitutive Laws.
Inviscid and real fluids 26
Introductory Notions of Thermodynamics.
First and Second Law of Thermodynamics 26
Constitutive (Behaviour, “Stresses-Deformations”
Relations) Laws 32
Inviscid (Ideal) Fluids 34
Real Fluids 38
vi
Shock Waves 43
The Unique Form of the Fluid Equations 49
2. DYNAMICS OF INVISCID FLUIDS 51
1 Vorticity and Circulation for Inviscid Fluids.
The Bernoulli Theorems 51
2 Some Simple Existence and Uniqueness Results 55