9 A Godunov-Type Method for a Multi-temperature Plasma …
123
a
b
Fig. 9.2 Evaluation of profiles of: a density, b temperatures of gas and radiation. Density profiles,
proton-electrons temperature profiles (circles), radiation temperature profiles (squares) at the contact
discontinuity decay with taking into account radiation. The gas velocity near the right boundary is
equaled v = −4 · 10 7 cm · s −1 and Mach number is equaled M = 16. Numbers indicate the time
moments: 5.36 · 10 −6 s (Eq. 9.1), 1.12 · 10 −5 s (Eq. 9.2), and 1.70 · 10 −5 s (Eq. 9.3)
ρ
a
b
Fig. 9.3 Steady solution of: a density profile, b proton-electrons temperature profile (circles) and
radiation temperature profile (squares) at SW with taking into account radiation at large time moment
more than 5 s. Used computational grid and the space scale cannot resolve nonequilibrium region
near SW with the size ∼ 10 4 cm. The jump of the radiation temperature on SW is an artifact of the
insufficient resolution of the grid
zone is considerable. The density after SW achieves the value of about 10
−5 g cm
−3
due to the radiation energy loss. The total adiabatic index for protons, electrons, and
radiation is less than value 5/3 for one atomic gas due to the considerable role of
radiation in the total energy.
The radiation flux plays considerable role not only in the relaxation zone. To
obtain a fine structure of the stationary SW on the distance ~1 mm at time moment
more than 10
−5 s, one should take into account radiation fluxes.
123
a
b
Fig. 9.2 Evaluation of profiles of: a density, b temperatures of gas and radiation. Density profiles,
proton-electrons temperature profiles (circles), radiation temperature profiles (squares) at the contact
discontinuity decay with taking into account radiation. The gas velocity near the right boundary is
equaled v = −4 · 10 7 cm · s −1 and Mach number is equaled M = 16. Numbers indicate the time
moments: 5.36 · 10 −6 s (Eq. 9.1), 1.12 · 10 −5 s (Eq. 9.2), and 1.70 · 10 −5 s (Eq. 9.3)
ρ
a
b
Fig. 9.3 Steady solution of: a density profile, b proton-electrons temperature profile (circles) and
radiation temperature profile (squares) at SW with taking into account radiation at large time moment
more than 5 s. Used computational grid and the space scale cannot resolve nonequilibrium region
near SW with the size ∼ 10 4 cm. The jump of the radiation temperature on SW is an artifact of the
insufficient resolution of the grid
zone is considerable. The density after SW achieves the value of about 10
−5 g cm
−3
due to the radiation energy loss. The total adiabatic index for protons, electrons, and
radiation is less than value 5/3 for one atomic gas due to the considerable role of
radiation in the total energy.
The radiation flux plays considerable role not only in the relaxation zone. To
obtain a fine structure of the stationary SW on the distance ~1 mm at time moment
more than 10
−5 s, one should take into account radiation fluxes.