Table 1 Computational details about the high-fidelity model and the model order reduction
Problem number | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
Space dimension | 2D | 2D | 2D | 3D |
IGA space dimension \((\mathcal {N}_v, \mathcal {N}_p)\) | (2178, 1024) | (2592, 1225) | (2178, 1024) | (6591, 343) |
Number of geometrical parameters | 2 rotations | 2 rotations | 4 rotations | 4 = 2 rotations+ outflow variation (length and width) |
Geometrical parameters range | \([-75 ^\circ , 75 ^\circ ]^2\) | \([-75 ^\circ , 75 ^\circ ]^2\) | \([-45 ^\circ , 45 ^\circ ]^4\) | \([-75 ^\circ , 75 ^\circ ]^2 \times [0,2]^2\) |
Number of IGA control points | 1089 | 1296 | 1089 | 2197 |
Number of FFD control points | 10 | 10 | 20 | 40 |
EIM tolerance | \(10^{-3}\) | \(10^{-3}\) | \(10^{-3}\) | \(10^{-3}\) |
EIM terms \(Q_K + Q_B + Q_f\) | 27 + 14 + 0 | 89 + 22 + 0 | 50 + 22 + 0 | 104 + 44 + 0 |
Number of snapshots | 500 | 500 | 500 | 500 |
POD tolerance I(N) | \(10^{-3}\) | \(10^{-2}\) | \(10^{-2}\) | \(2*10^{-2}\) |
POD space dimension \((N_{\mathbf {u},\mathbf {s}}, N_p)\) | (20, 10) | (20, 10) | (20, 10) | (40, 20) |
HF evaluation time | 1.5 s | 6.1 s | 1.5 s | 27 s |
POD offline construction time | 250 s | 2344 s | 250 s | 12325 s |
POD evaluation time | 0.07 s | 0.08 s | 0.08 s | 0.11 s |
Computational speedup POD | 20 | 76 | 18 | 245 |