Table 2
Accuracy values for the two-dimensional static ring problem for different sets of simulations varying the methods used, the time steps, and the resolution.
| Method | N × N | dt | Tmax | Tmin | L1 | k⊥,num/K|| |
|---|---|---|---|---|---|---|
| scheme #1 | 200 × 200 | dtTC | 10.166776 | 9.999981 | 7.600 × 10−5 | 1.5755 × 10−5 |
| scheme #1 | 300 × 300 | dtTC | 10.16678 | 10.0 | 8.016 × 10−5 | 1.2305 × 10−5 |
| scheme #1 | 400 × 400 | dtTC | 10.166782 | 10.0 | 8.188 × 10−5 | 1.0867 × 10−5 |
| scheme #1 | 500 × 500 | dtTC | 10.166783 | 10.0 | 8.288 × 10−5 | 1.0085 × 10−5 |
| scheme #2 | 200 × 200 | 10dtTC | 10.166772 | 9.999979 | 7.226 × 10−5 | 1.5751 × 10−5 |
| scheme #2 | 300 × 300 | 10dtTC | 10.16678 | 10.0 | 8.007 × 10−5 | 1.2305 × 10−5 |
| scheme #2 | 400 × 400 | 10dtTC | 10.16678 | 10.0 | 8.050 × 10−5 | 1.0866 × 10−5 |
| scheme #2 | 500 × 500 | 10dtTC | 10.166783 | 10.0 | 8.293 × 10−5 | 1.0085 × 10−5 |
| scheme #2 | 200 × 200 | 20dtTC | 10.166769 | 9.999979 | 6.941 × 10−5 | 1.5751 × 10−5 |
| scheme #2 | 300 × 300 | 20dtTC | 10.166779 | 10.0 | 7.881 × 10−5 | 1.2305 × 10−5 |
| scheme #2 | 400 × 400 | 20dtTC | 10.166781 | 10.0 | 8.120 × 10−5 | 1.0866 × 10−5 |
| scheme #2 | 500 × 500 | 20dtTC | 10.166782 | 10.0 | 8.247 × 10−5 | 1.0085 × 10−5 |
| scheme #2 | 200 × 200 | 30dtTC | 10.166767 | 9.999981 | 6.737 × 10−5 | 1.5751 × 10−5 |
| scheme #2 | 300 × 300 | 30dtTC | 10.166778 | 10.0 | 7.755 × 10−5 | 1.2305 × 10−5 |
| scheme #2 | 400 × 400 | 30dtTC | 10.16678 | 10.0 | 8.050 × 10−5 | 1.0866 × 10−5 |
| scheme #2 | 500 × 500 | 30dtTC | 10.166782 | 10.0 | 8.202 × 10−5 | 1.0085 × 10−5 |
Notes. In the fourth and fifth columns, the maximum and minimum temperatures at the final stage (t = 400) are given. The sixth column gives the error L1 for the maximum final temperature, obtained by comparing with the reference value T = 10.1667. Last column provides the ratio between the numerical perpendicular conductivity and the explicit parallel conductivity of k‖ = 0.01.
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