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

Convergence rates of some second and third order IMEX schemes for non equilibrium
initial data (dashed: v component, continuous: u component).
Convergence rate
Convergence rate
3
2.5
2
1.5
1
0.5
0
10 −6
−0.5
3
2.5
2
1.5
1
0.5
0
10 −5
−0.5
10 −5
10 −4
10 −4
10 −3
SSP2−222
10 −3
Epsilon
ARS−222
Epsilon
10 −2
10 −2
10 −1
10 −1
10 0
10 0
Convergence rate
4
3.5
3
2.5
2
1.5
1
0.5
0
10 −6
−0.5
Convergence rate
3
2.5
2
1.5
1
0.5
0
10 −6
−0.5
10 −5
10 −5
10 −4
10 −4
SSP3−332
10 −3
Epsilon
SSP2−322
10 −3
Epsilon
10 −2
10 −2
10 −1
10 −1
10 0
10 0
Convergence rate
4
3.5
3
2.5
2
1.5
1
0.5
0
10 −6
−0.5
Convergence rate
3
2.5
2
1.5
1
0.5
0
10 −6
−0.5
10 −5
10 −5
10 −4
10 −4
SSP3−443
10 −3
Epsilon
SSP2−332
10 −3
Epsilon
10 −2
10 −2
10 −1
10 −1
10 0
25
10 0