Page 8 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics
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Contents Vii
9.4 General Method for Determining of the Fluid Flow
Induced by the Displacement of an Arbitrary
System of Profiles Embedded in the Fluid in the
Presence of an “A Priori”
Given Basic Flow 105
10 Notions on the Steady Compressible Barotropic Flows 110
10.1. Immediate Consequences of the Bernoulli
Theorem 110
10.2. The Equation of Velocity Potential (Steichen) 113
10.3. Prandtl-Meyer (Simple Wave) Flow 115
10.4 Quasi-Uniform Steady Plane Flows 117
10.55 General Formulation of the Linearized Theory 118
10.6 Far Field (Infinity) Conditions 119
10.7 The Slip-Condition on the Obstacle 120
10.8 The Similitude of the Linearized Flows.
The Glauert—Prandtl Rule 121
11. Mach Lines. Weak Discontinuity Surfaces 123
12. Direct and Hodograph Methods for the Study of the
Compressible Inviscid Fluid Equations 127
12.1 A Direct Method [115] 128
12.2. Chaplygin Hodograph Method.
Molenbroek—Chaplygin equation 129
3. VISCOUS INCOMPRESSIBLE FLUID DYNAMICS 133
1 The Equation of Vorticity (Rotation) and the Circulation
Variation 133
2 Some Existence and Uniqueness Results 136
3 The Stokes System 138
4 Equivalent Formulations for the Navier-Stokes
Equations in Primitive Variables 140
4.1 Pressure Formulation 140
4.2 Pressure-Velocity Formulation 142
5 Equivalent Formulations for the Navier-Stokes
Equations in “Non-Primitive” Variables 143
5.1 Navier—Stokes Equations in Orthogonal Generalized
Coordinates, Stream Function Formulation 144
5.2 A “Coupled” Formulation in Vorticity and Stream
Function 151
5.3 The Separated (Uncoupled) Formulation in
Vorticity and Stream Function 152
