Page 7 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

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3.5 Shock Waves 43

3.6 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
Some Simple Existence and Uniqueness Results 55

Irrotational Flows of Incompressible Inviscid Fluids.
The Plane Case 59

Conformal Mapping and its Applications within Plane
Hydrodynamics 64
4.1 Helmholtz Instability 67

Principles of the (Wing) Profiles Theory 70

5.1 Flow Past a (Wing) Profile for an Incidence and
a Circulation “a priori’ Given 70
5.2 Profiles with Sharp Trailing Edge.
Joukovski Hypothesis 72
5.3 Theory of Joukovski Type Profiles 74

5.4 Example 77

5.5 An Iterative Method for Numerical Generation of
Conformal Mapping 79

Panel Methods for Incompressible Flow of Inviscid Fluid 81

6.1 The Source Panel Method for Non-Lifting Flows
Over Arbitrary Two-Dimensional Bodies 81
6.2 The Vortex Panel Method for Lifting Flows Over
Arbitrary Two-Dimensional Bodies 84

6.3 Example 87
Almost Potential Fluid Flow 92

Thin Profile Theory 95

8.1 Mathematical Formulation of the Problem 96
8.2 Solution Determination 97

Unsteady Irrotational Flows Generated by the Motion of
a Body in an Inviscid Incompressible Fluid 100
9.1 The 2-Dimensional (Plane) Case 100

9.2 The Determination of the Fluid Flow Induced by
the Motion of an Obstacle in the Fluid.
The Case of the Circular Cylinder 102
9.3 The 3-Dimensional Case 103