Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics
This handbook brings together the theoretical basics of fluid dynamics with a systemaic overview of the appropriate numerical and computational methods for solving the problems presented in the book. Also, effective codes for a majority of the exampl
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Numerical Methods and Algorithms Volume 3 Series Editor: Claude Brezinski Université des Sciences et Technologies de Lille, France
BASICS OF FLUID MECHANICS AND INTRODUCTION TO COMPUTATIONAL 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: Print ISBN:
0-387-23838-7 0-387-23837-9
©2005 Springer Science + Business Media, Inc. Print ©2005 Springer Science + Business Media, Inc. Boston All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America
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Contents
Preface 1. INTRODUCTION TO MECHANICS OF CONTINUA 1 Kinematics of Continua 1.1 The Concept of a Deformable Continuum Motion of a Continuum. 1.2 Lagrangian and Eulerian Coordinates Euler–Lagrange Criterion. 1.3 Euler’s and Reynolds’ (Transport) Theorems 2 General Principles. The Stress Tensor and Cauchy’s Fundamental Results The Forces Acting on a Continuum 2.1 Principle of Mass Conservation. 2.2 The Continuity Equation Principle of the Momentum Torsor Variation. 2.3 The Balance Equations 2.4 The Cauchy Stress Tensor The Cauchy Motion Equations 2.5 Principle of Energy Variation. 2.6 Conservation of Energy General Conservation Principle 2.7 3 Constitutive Laws. Inviscid and real fluids 3.1 Introductory Notions of Thermodynamics. First and Second Law of Thermodynamics 3.2 Constitutive (Behaviour, “Stresses-Deformations” Relations) Laws Inviscid (Ideal) Fluids 3.3 3.4 Real Fluids
xiii 1 1 1 4 13 17 17 18 20 21 23 24 25 26 26 32 34 38
vi 3.5 3.6
Shock Waves The Unique Form of the Fluid Equations
2. DYNAMICS OF INVISCID FLUIDS
43 49 51
Vorticity and Circulation for Inviscid Fluids. The Bernoulli Theorems
51
2
Some Simple Existence and Uniqueness Results
55
3
Irrotational Flows of Incompressible Inviscid Fluids. The Plane Case Conformal Mapping and its Applications within Plane Hydrodynamics 4.1 Helmholtz Instability
1
4
59 64 67
Principles of the (Wing) Profiles Theory 5.1 Flow Past a (Wing) Profile for an Incidence and a Circulation “a priori” Given Profiles with Sharp Trailing Edge. 5.2 Joukovski Hypothesis 5.3 Theory of Joukovski Type Profiles Example 5.4 An Iterative Method for Numerical Generation of 5.5 Conformal Mapping
70
Panel Methods for Incompressible Flow of Inviscid Fluid 6.1 The Source Panel Method for Non-Lifting Flows Over Arbitrary Two-Dimensional Bodies 6.2 The Vortex Panel Method for Lifting Flows Over Arbitrary Two-Dimensional Bodies 6.3 Example
81
7
Almost Potential Fluid Flow
92
8
Thin Profile Theory 8.1 Mathematical Formulation of the Problem 8.2 Solution Determination Unsteady Irrotational Flows Generated by the Motion of a Body in an Inviscid Incompre
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