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Table C.1
Error norms of the density field, and derived orders of accuracy for the combinations of dicretization schemes applied to the isentropic vortex problem as described in the text.
| SLIP unlimited scheme | SLIP limited scheme (ν = 2) | ||||||
| L2-norm | Error | Observed | L2-norm | Error | Observed | ||
| Mesh | Δt | of error | ratio | order | of error | ratio | order |
|
|
|||||||
| ESDIRK23 stepping | |||||||
| 16 × 16 | 4.00E-01 | 8.083686E-04 | – | – | 1.195121E-03 | – | – |
| 32 × 32 | 2.00E-01 | 1.829503E-04 | 4.419 | 2.14 | 5.355714E-04 | 2.231 | 1.16 |
| 64 × 64 | 1.00E-01 | 3.918942E-05 | 4.668 | 2.22 | 1.771569E-04 | 3.023 | 1.60 |
| 128 × 128 | 5.00E-02 | 8.995759E-06 | 4.356 | 2.12 | 3.806272E-05 | 4.654 | 2.22 |
| 256 × 256 | 2.50E-02 | 2.165725E-06 | 4.154 | 2.05 | 7.076837E-06 | 5.378 | 2.43 |
| 512 × 512 | 1.25E-02 | 5.327543E-07 | 4.065 | 2.02 | 1.433251E-06 | 4.938 | 2.30 |
|
|
|||||||
| ESDIRK46 stepping | |||||||
| 16 × 16 | 4.00E-01 | 8.305988E-04 | – | – | 1.225907E-03 | – | – |
| 64 × 64 | 2.00E-01 | 3.909528E-05 | 21.246 | 4.41 | 1.826213E-04 | 6.713 | 2.75 |
| 256 × 256 | 1.00E-01 | 2.151586E-06 | 18.170 | 4.18 | 7.185873E-06 | 25.414 | 4.67 |
| 1024 × 1024 | 5.00E-02 | 1.315482E-07 | 16.356 | 4.03 | 2.940004E-07 | 24.442 | 4.61 |
Notes. In case of the ESDIRK46-based schemes, the listed order refers solely to the temporal discretization.
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