Linked e-resources
Details
Table of Contents
Intro
Preface
Contents
About the Author
Introduction
1. Scope of the Dynamics of Compressible Fluids
2. The Subject Matter of Dynamics of Compressible Fluids
1 General Equations of Gas Motion
1.1 The Thermodynamic Model of a Perfect Gas
Adiabatic Formulae
1.1.1 Internal State of a Gas Particle
Thermodynamic Variables
1.1.2 Perfect Gas Model
Polytropic Gas
1.1.3 Adiabatic Formulae
1.2 Governing Equations of Gas Motion
Mathematical Model ...
1.3 Speed of Propagation of Small Disturbances in Ideal Gas
Sound Speed
1.4 Thermodynamics of a Moving Gas
1.4.1 Bernoulli-Saint-Venant Equation
Enthalpy
1.4.2 Stagnation Gas State
Isentropic Formulae
1.4.3 Laval's Number
Other Characteristic States of a Moving Gas
References
2 Continuous Flows
2.1 Equations of One-Dimensional Steady Gas Flow
Rule of a Stream Reversal
2.2 Gas Outflow from Reservoir
Saint-Venant-Vantzel Formula
2.3 Supersonic Outflow Mode
Laval's Nozzle
References
3 Discontinuity in a Gas Flow
3.1 Conservation Laws at a Strong Discontinuity Surface
3.2 Classification of Strong Discontinuities
Shocks
3.3 Normal Shock Theory
3.4 Normal Shock Regularities
3.4.1 Velocity Jump
3.4.2 Pressure Jump
3.4.3 Density Jump
3.4.4 Entropy Jump
3.5 Shock Adiabatic Curve and Its Properties
3.5.1 Equation of Shock Adiabatic Curve
3.5.2 ``Asterisk'' Property
3.5.3 Limiting Degree of Gas Compression in Shock Waves
3.5.4 Approximation of Strong Shocks
3.5.5 Approximation of Weak Shocks
References
4 Governing Equations and Initial-Boundary-Value Problems
4.1 Geometry of One-Dimensional Flows
4.2 Equations of Motion in Euler's Form
Initial and Boundary Conditions
4.2.1 Euler's Equations of Motion
4.2.2 Initial Conditions
4.2.3 Boundary Conditions
4.3 Equations of Motion in Lagrange's Form
4.4 Equations of Motion in Characteristic Form
the Characteristic ...
4.5 The Method of Characteristics
4.6 Generalized Cauchy Problem (Type I Problem) ...
4.7 The Goursat Problem (Type II Problem)
4.8 Combined Problem of a Special Type (Type III Problem)
4.9 Characteristics as Trajectories of a Possible Weak Discontinuity of a Solution
4.9.1 Relationships Along the Weak Discontinuity Trajectory
Preface
Contents
About the Author
Introduction
1. Scope of the Dynamics of Compressible Fluids
2. The Subject Matter of Dynamics of Compressible Fluids
1 General Equations of Gas Motion
1.1 The Thermodynamic Model of a Perfect Gas
Adiabatic Formulae
1.1.1 Internal State of a Gas Particle
Thermodynamic Variables
1.1.2 Perfect Gas Model
Polytropic Gas
1.1.3 Adiabatic Formulae
1.2 Governing Equations of Gas Motion
Mathematical Model ...
1.3 Speed of Propagation of Small Disturbances in Ideal Gas
Sound Speed
1.4 Thermodynamics of a Moving Gas
1.4.1 Bernoulli-Saint-Venant Equation
Enthalpy
1.4.2 Stagnation Gas State
Isentropic Formulae
1.4.3 Laval's Number
Other Characteristic States of a Moving Gas
References
2 Continuous Flows
2.1 Equations of One-Dimensional Steady Gas Flow
Rule of a Stream Reversal
2.2 Gas Outflow from Reservoir
Saint-Venant-Vantzel Formula
2.3 Supersonic Outflow Mode
Laval's Nozzle
References
3 Discontinuity in a Gas Flow
3.1 Conservation Laws at a Strong Discontinuity Surface
3.2 Classification of Strong Discontinuities
Shocks
3.3 Normal Shock Theory
3.4 Normal Shock Regularities
3.4.1 Velocity Jump
3.4.2 Pressure Jump
3.4.3 Density Jump
3.4.4 Entropy Jump
3.5 Shock Adiabatic Curve and Its Properties
3.5.1 Equation of Shock Adiabatic Curve
3.5.2 ``Asterisk'' Property
3.5.3 Limiting Degree of Gas Compression in Shock Waves
3.5.4 Approximation of Strong Shocks
3.5.5 Approximation of Weak Shocks
References
4 Governing Equations and Initial-Boundary-Value Problems
4.1 Geometry of One-Dimensional Flows
4.2 Equations of Motion in Euler's Form
Initial and Boundary Conditions
4.2.1 Euler's Equations of Motion
4.2.2 Initial Conditions
4.2.3 Boundary Conditions
4.3 Equations of Motion in Lagrange's Form
4.4 Equations of Motion in Characteristic Form
the Characteristic ...
4.5 The Method of Characteristics
4.6 Generalized Cauchy Problem (Type I Problem) ...
4.7 The Goursat Problem (Type II Problem)
4.8 Combined Problem of a Special Type (Type III Problem)
4.9 Characteristics as Trajectories of a Possible Weak Discontinuity of a Solution
4.9.1 Relationships Along the Weak Discontinuity Trajectory