Table 2.
Comparison of L 2-norm errors for the corresponding vortex fields. The third and fourth columns represent normalized L 2-norm errors for pointwise and global energy estimates of vorticity. Here, Δω = ω recon − ω exact and Δk ω/k ω exact = |‖ω exact‖2 − ‖ω recon‖2|/‖ω exact‖2.
| t/T | ‖ω exact‖2 | ‖ω recon‖2 | ‖Δω‖2/‖ω exact‖2 | Δk ω/k ω exact |
|
| ||||
| 0.1 | 1.09 | 1.19 | 36.8% | 8.7% |
| 0.2 | 2.35 | 2.48 | 24.7% | 5.3% |
| 0.3 | 2.82 | 2.90 | 21.7% | 2.8% |
| 0.4 | 2.31 | 2.34 | 21.2% | 1.4% |
| 0.5 | 1.67 | 1.67 | 32.1% | 0.4% |
| 0.6 | 1.38 | 1.40 | 40.6% | 1.7% |
| 0.7 | 1.33 | 1.40 | 46.7% | 5.2% |
| 0.8 | 1.20 | 1.30 | 51.4% | 7.8% |
| 0.9 | 0.95 | 1.02 | 52.0% | 6.7% |
| 1.0 | 0.79 | 0.82 | 47.8% | 4.2% |