Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
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Monatomic gas in Extended Thermodynamics<br />
U =<br />
⎛<br />
⎜<br />
⎝<br />
ρ<br />
ρv<br />
1<br />
2ρv2 + 3<br />
Ut + F (U)x = 1<br />
ɛ R(U)<br />
2 p<br />
2<br />
3 ρv2 + σ<br />
ρv 3 + 5vp + 2σv + 2q<br />
F =<br />
⎛<br />
⎜<br />
⎝<br />
⎞<br />
⎛<br />
⎟<br />
⎜<br />
⎟<br />
⎜<br />
⎟ , R = − ⎜<br />
⎠<br />
⎝<br />
ρv<br />
ρv2 + p + σ<br />
vp + σv + q<br />
2<br />
3<br />
0<br />
0<br />
0<br />
ρσ<br />
ρ(2q + 3vσ)<br />
1<br />
2ρv3 + 5<br />
2<br />
2<br />
3ρv3 + 4 7 8<br />
vp + vσ + 3 3 15q ρv4 + 5 p2<br />
32<br />
+ 7σp + ρ ρ 5 qv + v2 (8p + 5σ)<br />
ρ: density, u: velocity, p: pressure, σ: stress, q: heat flux<br />
As ɛ → 0 ⇒ σ → 0, q → 0 we obtain the Euler equations <strong>for</strong> monatomic gas.<br />
We use IMEX-SSP2(2,2,2) central scheme <strong>for</strong> a generalization of classical Sod’s problem<br />
U = Ul = (1, 0, 5, 0, 0), x < 0.5,<br />
U = Ur = (0.125, 0, 0.5, 0, 0), x > 0.5.<br />
⎞<br />
⎟<br />
⎠<br />
⎞<br />
⎟<br />
⎠ ,<br />
30