|
2D isentropic vortex problem
|
|---|
| |
\(\boldsymbol{N}_{\boldsymbol{x}}\)
|
ADER-Prim
|
ADER-Cons
|
ADER-Char
|
Theor.
|
|---|
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
error
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
order
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
error
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
order
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
error
|
\(\boldsymbol{L}_{\boldsymbol{2}}\)
order
|
|---|
|
\(\mathbb{P}_{0}\mathbb{P}_{2}\)
|
100
|
4.060E-03
|
-
|
5.028E-03
|
-
|
5.010E-03
|
-
|
3
|
|
120
|
2.359E-03
|
2.98
|
2.974E-03
|
2.88
|
2.968E-03
|
2.87
|
|
140
|
1.489E-03
|
2.98
|
1.897E-03
|
2.92
|
1.893E-03
|
2.92
|
|
160
|
9.985E-04
|
2.99
|
1.281E-03
|
2.94
|
1.279E-03
|
2.94
|
|
200
|
5.118E-04
|
2.99
|
6.612E-04
|
2.96
|
6.607E-04
|
2.96
|
|
\(\mathbb{P}_{0}\mathbb{P}_{3}\)
|
50
|
2.173E-03
|
-
|
4.427E-03
|
-
|
5.217E-03
|
-
|
4
|
|
60
|
8.831E-04
|
4.93
|
1.721E-03
|
5.18
|
2.232E-03
|
4.65
|
|
70
|
4.177E-04
|
4.85
|
8.138E-04
|
4.85
|
1.082E-03
|
4.69
|
|
80
|
2.194E-04
|
4.82
|
4.418E-04
|
4.57
|
5.746E-04
|
4.74
|
|
100
|
7.537E-05
|
4.79
|
1.605E-04
|
4.53
|
1.938E-04
|
4.87
|
|
\(\mathbb{P}_{0}\mathbb{P}_{4}\)
|
50
|
2.165E-03
|
-
|
3.438E-03
|
-
|
3.416E-03
|
-
|
5
|
|
60
|
6.944E-04
|
6.23
|
1.507E-03
|
4.52
|
1.559E-03
|
4.30
|
|
70
|
3.292E-04
|
4.84
|
7.615E-04
|
4.43
|
7.615E-04
|
4.65
|
|
80
|
1.724E-04
|
4.84
|
4.149E-04
|
4.55
|
4.148E-04
|
4.55
|
|
100
|
5.884E-05
|
4.82
|
1.449E-04
|
4.71
|
1.448E-04
|
4.72
|
- A comparison is shown among the reconstruction in primitive variables (ADER-Prim), in conserved variables (ADER-Cons) and in characteristic variables (ADER-Char). The Osher-type numerical flux has been used.
