This is one of the standard test cases for laminar twodimensional flow.
We run this experiment with the following configuration
- equidistant grids with a resolution of 48x48 and 96x96 cells
- timestep sizes of 0.005 and 0.002, computation into the stationary limit
- Reynolds number 1000
- VONOS scheme for the convective term
- BiCGStab solver for the pressure poisson equation
Left: vorticity, Right: streamfuntion.
Horizontal velocity u through the vertical centerline in comparison with [1],[2]
| y | [1] | [2] | 48x48 | 96x96 | '48x48'-[2] | '96x96'-[2] | ratio error |
| 1.0000 | -1.0000 | -1.0000 | -1.0000 | -1.0000 | 0.0000 | 0.0000 | / |
| 0.9766 | -0.6593 | -0.6644 | -0.6421 | -0.6587 | 0.0224 | 0.0057 | 3.8913 |
| 0.9688 | -0.5749 | -0.5808 | -0.5447 | -0.5772 | 0.0362 | 0.0036 | 10.0099 |
| 0.9609 | -0.5112 | -0.5169 | -0.5002 | -0.5132 | 0.0167 | 0.0037 | 4.4722 |
| 0.9531 | -0.4660 | -0.4723 | -0.4566 | -0.4673 | 0.0157 | 0.0050 | 3.1454 |
| 0.8516 | -0.3330 | -0.3372 | -0.3220 | -0.3354 | 0.0153 | 0.0018 | 8.4640 |
| 0.7344 | -0.1872 | -0.1887 | -0.1799 | -0.1873 | 0.0088 | 0.0014 | 6.2185 |
| 0.6172 | -0.0570 | -0.0570 | -0.0530 | -0.0560 | 0.0040 | 0.0010 | 3.8762 |
| 0.5000 | 0.0608 | 0.0621 | 0.0616 | 0.0628 | -0.0004 | 0.0008 | 0.5658 |
| 0.4531 | 0.1065 | 0.1082 | 0.1061 | 0.1089 | -0.0021 | 0.0007 | 2.9986 |
| 0.2813 | 0.2781 | 0.2804 | 0.2734 | 0.2807 | -0.0069 | 0.0003 | 23.8491 |
| 0.1719 | 0.3829 | 0.3886 | 0.3703 | 0.3886 | -0.0183 | 0.0001 | 305.8935 |
| 0.1016 | 0.2973 | 0.3005 | 0.2667 | 0.2905 | -0.0337 | -0.0099 | 3.4017 |
| 0.0703 | 0.2222 | 0.2229 | 0.1923 | 0.2116 | -0.0306 | -0.0113 | 2.7124 |
| 0.0625 | 0.2020 | 0.2023 | 0.1734 | 0.1912 | -0.0290 | -0.0111 | 2.6046 |
| 0.0547 | 0.1811 | 0.1813 | 0.1544 | 0.1706 | -0.0269 | -0.0107 | 2.5063 |
Vertical velocity v tdrough tde horizontal centerline in comparison witd [1],[2]
| x | [1] | [2] | 48x48 | 96x96 | '48x48'-[2] | '96x96'-[2] | ratio error |
| 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | / |
| 0.031200 | -0.213880 | -0.227923 | -0.215317 | -0.215670 | 0.012605 | 0.012252 | 1.028833 |
| 0.039100 | -0.276690 | -0.293687 | -0.273664 | -0.279071 | 0.020023 | 0.014616 | 1.369999 |
| 0.046900 | -0.337140 | -0.355321 | -0.331272 | -0.340443 | 0.024050 | 0.014878 | 1.616433 |
| 0.054700 | -0.391880 | -0.410375 | -0.383090 | -0.394827 | 0.027285 | 0.015548 | 1.754893 |
| 0.093700 | -0.515500 | -0.526439 | -0.491542 | -0.521092 | 0.034897 | 0.005347 | 6.526169 |
| 0.140600 | -0.426650 | -0.426455 | -0.407328 | -0.425523 | 0.019126 | 0.000931 | 20.535372 |
| 0.195300 | -0.319660 | -0.320214 | -0.304612 | -0.319046 | 0.015602 | 0.001168 | 13.359297 |
| 0.500000 | 0.025260 | 0.025799 | 0.025014 | 0.024648 | -0.000786 | -0.001151 | 0.682528 |
| 0.765600 | 0.322350 | 0.325359 | 0.310265 | 0.322496 | -0.015094 | -0.002863 | 5.271553 |
| 0.773400 | 0.330750 | 0.333992 | 0.318338 | 0.331114 | -0.015654 | -0.002878 | 5.438887 |
| 0.843700 | 0.370950 | 0.376919 | 0.357302 | 0.375189 | -0.019617 | -0.001730 | 11.338475 |
| 0.906200 | 0.326270 | 0.333044 | 0.309373 | 0.329850 | -0.023671 | -0.003194 | 7.410599 |
| 0.921900 | 0.303530 | 0.309910 | 0.285914 | 0.306744 | -0.023996 | -0.003166 | 7.579356 |
| 0.929700 | 0.290120 | 0.296270 | 0.272875 | 0.292810 | -0.023395 | -0.003460 | 6.761235 |
| 0.937500 | 0.274850 | 0.280706 | 0.257110 | 0.277076 | -0.023595 | -0.003629 | 6.501094 |
[1] Ghia U.,Ghia K., Shin C., High-Re solutions for incompressible flow using tde Navier Stokes eqs., JCP 1982, 48, pp. 387-411
[2] Benchmark spectral results on tde lid-driven cavity flow, Botella O., Peyret R., Computers & Fluids 19998, 27, pp. 421-433
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