Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti

Initial layer fix
Next, we test the schemes with following two Riemann problems
ρ(x,t)
2.05
2
ρl = 2, ml = 1, zl = 1, x < 0.2,
ρr = 1, mr = 0.13962, zr = 1, x > 0.2,
ρl = 1, ml = 0, zl = 1, x < 0,
ρr = 0.2, mr = 0, zr = 1, x > 0.
ε=1e−008, t=0.50, N=200
1.95
−0.2 −0.15 −0.1 −0.05 0
x
0.05 0.1 0.15 0.2
−1
−2
−3
−4
x
ε=1e−008,
10−3
5
4
3
2
1
0
t=0.25, N=200
−5
0.2 0.25 0.3 0.35
x
0.4 0.45 0.5
Initial layer for ρ in problem 1 (left) and departure from equilibrium z − zE in problem 2 (right) for ε =
10 −8 . Left problem: ARS(2,2,2) (∗), ARSF(2,2,2) (◦), IMEX-SSP2(2,2,2) (×). Right problem: IMEX-
SSP2(2,2,2) (+), IMEX-SSP2F(2,2,2) (×), ARS(2,2,2) (◦).
z(x,t)−z E (x,t)
29
(1)
(2)