Table 5 Influence of the order-approximation of \(1/\mu \)—one layer \([0^{\circ } ]\) - \(S=4\)—mesh 26 \(\times \) 10—numerical layers \(N_z = 4 \times NC\)
\(\varvec{\phi }\) | Expansion | Model | \(\bar{{{\varvec{u}}}}{{\varvec{(0,e/2)}}}\) max | \(\bar{{{\varvec{w}}}}{{\varvec{(L,0)}}}\) | \(\bar{\varvec{\sigma }}_{{{\varvec{11}}}}{{\varvec{(-e/2)}}}\) | \(\bar{\varvec{\sigma }}_{{{\varvec{13}}}}{{\varvec{(0)}}}\) | \(\bar{\varvec{\sigma }}_{{{\varvec{33}}}}\) max |
|---|---|---|---|---|---|---|---|
\(\phi =\pi /8\) | Zero-order | VS-LM4 | \(-\) 0.0085 | 0.0211 | \(-\) 0.2094 | 0.1415 | 1.0027 |
Error | 9.30% | 11.86% | 21.63% | 11.44% | 0.27% | ||
One-order | VS-LM4 | \(-\) 0.0096 | 0.0243 | \(-\) 0.2694 | 0.1621 | 1.0103 | |
Error | 2.59% | 1.30% | 0.82% | 1.48% | 1.03% | ||
Two-order | VS-LM4 | \(-\) 0.0095 | 0.0241 | \(-\) 0.2670 | 0.1616 | 1.0023 | |
Error | 1.72% | 0.46% | 0.09% | 1.14% | 0.23% | ||
Exact | \(-\) 0.0094 | 0.0240 | \(-\) 0.2673 | 0.1597 | 1.0000 | ||
\(\phi =\pi /3 \) | Zero-order | VS-LM4 | 2.3664 | 0.2797 | \(-\) 1.0442 | 0.5119 | 1.0101 |
Error | 10.39% | 10.32% | 21.54% | 10.80% | 1.01% | ||
One-order | VS-LM4 | 2.6764 | 0.3160 | \(-\) 1.3518 | 0.5766 | 1.0221 | |
Error | 1.35% | 1.30% | 1.57% | 0.49% | 2.21% | ||
Two-order | VS-LM4 | 2.6411 | 0.3119 | \(-\) 1.3329 | 0.5720 | 1.0110 | |
Error | 0.01% | 0.02% | 0.16% | 0.32% | 1.10% | ||
Exact | 2.6408 | 0.3120 | \(-\) 1.3309 | 0.5739 | 1.0000 |