E
Energy balance equation, 17–21
Energy equation, 287
Energy of the explosion, 229–231
Entropy change for weak shocks, 12, 21, 23–24,
99–102, 105–108, 121, 122
Entropy changes, ideal gas, 23
Entropy increase across a shock
gas, 106
mass, 106
normal shock, 107
second law of thermodynamics, 106, 108
symmetric, Match number, 105
Equations of fluid flow
artificial viscosity, 2
conservation equations, plane geometry
(see Plane geometry)
constancy of entropy with time, 21
elements, thermodynamics
(see Thermodynamics of perfect
gases)
entropy changes, 23
gradients, 1
Lagrangian and Eulerian systems
(see Eulerian and Lagrangian form of
the equations)
physical effects, 1
shocks, 2
small amplitude disturbances (see Small
amplitude disturbances)
Spherical geometry (see Spherical
geometry)
viscosity, 2
Eulerian and Lagrangian form of the equations
acceleration, 2, 3
caloric equation of state, 2
description, motion, 2
equation of state, 2
fluid/gas motion, 2
ideal gas, 2
material derivative, 2
spatial variation, velocity, 3
velocity, 2
Expanding spherical shock wave, 282, 299
See also Expansion of an isothermal sphere
Expansion fan, 78, 170–173
Expansion of an isothermal sphere
density, as a function of normalised radius
during early stages, 303, 308
during very early stages, 308
during very late stages, 304, 309
Normalized time, pressure at, 307
particle velocity, as a function of normalised
radius
during earliest stages, 309
during early stages, 310
during later stages, 311
during late stages, 304, 310
pressure, as a function of normalised radius
during continued expansion, 306
during earliest stages, 302, 303
during early stages, 304
during late stages, 303, 306
during much later stages, 307
Expansion wave, 170–175
Explosion energy, 255
F
Finite difference equations, 131, 132,
146, 148
First law of thermodynamics, 4
Fourier components, 187
Friedrichs’ analysis, 195, 196, 199, 200
Friedrichs’ theory, 199, 200
G
Grid size, 311
Grid spacing, 152
H
Heat capacity, 4–6
Heat energy, 229, 244
I
Impulsive piston motion, 192, 193
Incident shock wave, 110, 111, 113, 115
Incremental piston motion, 177, 187–189
Incremental velocity, 188
Isothermal expansion/compression
of ideal gas, 7
Isothermal sphere, 300
See also Expansion of an isothermal
sphere
K
Kelvin-Planck statement, 11
Kinetic energy, 229, 255, 259
Kinetic theory of gases, 10
340
Index
Energy balance equation, 17–21
Energy equation, 287
Energy of the explosion, 229–231
Entropy change for weak shocks, 12, 21, 23–24,
99–102, 105–108, 121, 122
Entropy changes, ideal gas, 23
Entropy increase across a shock
gas, 106
mass, 106
normal shock, 107
second law of thermodynamics, 106, 108
symmetric, Match number, 105
Equations of fluid flow
artificial viscosity, 2
conservation equations, plane geometry
(see Plane geometry)
constancy of entropy with time, 21
elements, thermodynamics
(see Thermodynamics of perfect
gases)
entropy changes, 23
gradients, 1
Lagrangian and Eulerian systems
(see Eulerian and Lagrangian form of
the equations)
physical effects, 1
shocks, 2
small amplitude disturbances (see Small
amplitude disturbances)
Spherical geometry (see Spherical
geometry)
viscosity, 2
Eulerian and Lagrangian form of the equations
acceleration, 2, 3
caloric equation of state, 2
description, motion, 2
equation of state, 2
fluid/gas motion, 2
ideal gas, 2
material derivative, 2
spatial variation, velocity, 3
velocity, 2
Expanding spherical shock wave, 282, 299
See also Expansion of an isothermal sphere
Expansion fan, 78, 170–173
Expansion of an isothermal sphere
density, as a function of normalised radius
during early stages, 303, 308
during very early stages, 308
during very late stages, 304, 309
Normalized time, pressure at, 307
particle velocity, as a function of normalised
radius
during earliest stages, 309
during early stages, 310
during later stages, 311
during late stages, 304, 310
pressure, as a function of normalised radius
during continued expansion, 306
during earliest stages, 302, 303
during early stages, 304
during late stages, 303, 306
during much later stages, 307
Expansion wave, 170–175
Explosion energy, 255
F
Finite difference equations, 131, 132,
146, 148
First law of thermodynamics, 4
Fourier components, 187
Friedrichs’ analysis, 195, 196, 199, 200
Friedrichs’ theory, 199, 200
G
Grid size, 311
Grid spacing, 152
H
Heat capacity, 4–6
Heat energy, 229, 244
I
Impulsive piston motion, 192, 193
Incident shock wave, 110, 111, 113, 115
Incremental piston motion, 177, 187–189
Incremental velocity, 188
Isothermal expansion/compression
of ideal gas, 7
Isothermal sphere, 300
See also Expansion of an isothermal
sphere
K
Kelvin-Planck statement, 11
Kinetic energy, 229, 255, 259
Kinetic theory of gases, 10
340
Index