Open Access
Table F.1.
Data obtained from dimension reduction compared to values obtained for the full 2D problem with the DROP code, obtained for several surface axis ratios 
and polytropic indices n. The computing times spent to achieve convergence are purely indicative, and may vary a little with the computer load.
| N | n |
 |
iterations | comp. time (s) |  |
Ω2/(Gρc) | |VP/W| | RMS | |
|---|---|---|---|---|---|---|---|---|---|
| this work | 256 | 1.5 | 0.950 | 32 | 0.199 | 6.492 × 10−1 | 5.314 × 10−2 | 1 × 10−4 | 4 × 10−5 |
| DROP code | 32 | 37.0 | 6.490 × 10−1 | 5.310 × 10−2 | 1 × 10−5 | ||||
| 256 | 1.5 | 0.900 | 33 | 0.217 | 5.979 × 10−1 | 1.034 × 10−1 | 5 × 10−4 | 2 × 10−4 | |
| 44 | 48.4 | 5.973 × 10−1 | 1.032 × 10−1 | 1 × 10−5 | |||||
| 256 | 1.5 | 0.850 | 35 | 0.230 | 5.452 × 10−1 | 1.501 × 10−1 | 1 × 10−3 | 4 × 10−4 | |
| 42 | 46.6 | 5.437 × 10−1 | 1.497 × 10−1 | 1 × 10−5 | |||||
| 256 | 1.5 | 0.800 | 37 | 0.249 | 4.906 × 10−1 | 1.921 × 10−1 | 2 × 10−3 | 7 × 10−4 | |
| 42 | 46.1 | 4.881 × 10−1 | 1.912 × 10−1 | 1 × 10−5 | |||||
| 256 | 1.5 | 0.750 | 39 | 0.261 | 4.339 × 10−1 | 2.280 × 10−1 | 3 × 10−3 | 1 × 10−3 | |
| 44 | 48.0 | 4.302 × 10−1 | 2.266 × 10−1 | 1 × 10−5 | |||||
| 256 | 1.5 | 0.700 | 43 | 0.285 | 3.747 × 10−1 | 2.561 × 10−1 | 5 × 10−3 | 2 × 10−3 | |
| 56 | 59.7 | 3.698 × 10−1 | 2.538 × 10−1 | 2 × 10−5 | |||||
| 256 | 1.5 | 0.650 | 50 | 0.327 | 3.126 × 10−1 | 2.736 × 10−1 | 6 × 10−3 | 2 × 10−3 | |
| 56 | 58.2 | 3.071 × 10−1 | 2.704 × 10−1 | 2 × 10−5 | |||||
| 256 | 1.5 | 0.617 | 50 | 0.324 | 2.701 × 10−1 | 2.777 × 10−1 | 6 × 10−3 | 2 × 10−3 | |
| 74 | 73.3 | 2.648 × 10−1 | 2.740 × 10−1 | 2 × 10−5 | |||||
| this work | 256 | 0.5 | 0.950 | 16 | 0.102 | 2.162 | 1.189 × 10−1 | 5 × 10−4 | 7 × 10−4 |
| DROP code | 23 | 28.5 | 2.162 | 1.189 × 10−1 | 3 × 10−4 | ||||
| 256 | 1.0 | 0.950 | 24 | 0.152 | 1.197 | 8.259 × 10−2 | 1 × 10−4 | 7 × 10−5 | |
| 51 | 56.4 | 1.197 | 8.253 × 10−1 | 2 × 10−5 | |||||
| 256 | 2.0 | 0.950 | 40 | 0.244 | 3.359 × 10−1 | 3.089 × 10−2 | 1 × 10−4 | 3 × 10−5 | |
| 44 | 47.3 | 3.358 × 10−1 | 3.087 × 10−2 | 1 × 10−5 | |||||
| 256 | 2.5 | 0.950 | 51 | 0.306 | 1.610 × 10−1 | 1.589 × 10−2 | 8 × 10−5 | 4 × 10−5 | |
| 50 | 53.5 | 1.610 × 10−1 | 1.589 × 10−2 | 3 × 10−5 | |||||
| 256 | 3.0 | 0.950 | 70 | 0.425 | 6.859 × 10−2 | 7.032 × 10−3 | 8 × 10−5 | 5 × 10−5 | |
| 65 | 68.1 | 6.853 × 10−2 | 7.023 × 10−3 | 4 × 10−5 | |||||
| 256 | 3.5 | 0.950 | 88 | 0.516 | 2.402 × 10−2 | 2.507 × 10−3 | 1 × 10−4 | 1 × 10−4 | |
| 88 | 91.0 | 2.398 × 10−2 | 2.501 × 10−3 | 7 × 10−5 | |||||
| 256 | 4.0 | 0.950 | 127 | 0.750 | 5.861 × 10−3 | 6.163 × 10−4 | 4 × 10−4 | 2 × 10−4 | |
| 128 | 130 | 5.818 × 10−3 | 6.112 × 10−4 | 2 × 10−4 | |||||
| this work | 32 | 1.5 | 0.950 | 31 | 0.004 | 6.505 × 10−1 | 5.336 × 10−2 | 5 × 10−4 | 5 × 10−4 |
| DROP code | 34 | 0.067 | 6.483 × 10−1 | 5.307 × 10−2 | 8 × 10−4 | ||||
| 64 | 1.5 | 0.950 | 31 | 0.014 | 6.496 × 10−1 | 5.320 × 10−2 | 2 × 10−4 | 1 × 10−4 | |
| 34 | 0.497 | 6.489 × 10−1 | 5.308 × 10−2 | 2 × 10−4 | |||||
| 128 | 1.5 | 0.950 | 31 | 0.050 | 6.493 × 10−1 | 5.315 × 10−2 | 1 × 10−4 | 6 × 10−5 | |
| 35 | 5.10 | 6.490 × 10−1 | 5.310 × 10−2 | 5 × 10−5 | |||||
| 512 | 1.5 | 0.950 | 31 | 0.783 | 6.493 × 10−1 | 5.314 × 10−2 | 1 × 10−4 | 4 × 10−5 | |
| 33 | 346 | 6.490 × 10−1 | 5.311 × 10−2 | 3 × 10−6 | |||||
| this work | 1024 | 1.5 | 0.950 | 31 | 2.97 | 6.492 × 10−1 | 5.314 × 10−2 | 1 × 10−4 | |
| this work | 2048 | 1.5 | 0.950 | 31 | 11.9 | 6.492 × 10−1 | 5.314 × 10−2 | 1 × 10−4 |
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