FSI tests

The following FSI tests are performed for two different inflow speeds. FSI1 is resulting in a steady state solution, while the other two tests (FSI2, FSI3) result in periodic solutions and correspond to the final benchmark settings.

Parameter settings for the full FSI benchmarks
parameter FSI1 FSI2 FSI3
$\varrho^s$ [$10^3 \frac{\textrm{kg}\nop}{\textrm{m}^3}$] 1 10 1
$\nu^s$ 0.4 0.4 0.4
$\mu^s$ [$10^6 \frac{\textrm{kg}\nop}{\textrm{ms}^2}$] 0.5 0.5 2.0
$\varrho^f$ [ $10^3 \frac{\textrm{kg}\nop}{\textrm{m}^3}$ ] 1 1 1
$\nu^f$ [ $10^{-3} \frac{\textrm{m}^2}{\textrm{s}\nop}$ ] 1 1 1
$\bar{U}$ [ $\frac{\textrm{m}\nop}{\textrm{s}}$ ] 0.2 1 2
parameter FSI1 FSI2 FSI3
$\beta=\frac{\varrho^s}{\varrho^f}$ 1 10 1
$\nu^s$ 0.4 0.4 0.4
$\textrm{Ae}=\frac{E^s}{\varrho^f \bar{U}^2}$ 3.5 × 104 1.4 × 103 1.4 × 103
$\Re=\frac{\bar{U} d}{\nu^f}$ 20 100 200
$\bar{U}$ 0.2 1 2

Results for FSI1
level nel ndof ux(A) uy(A) drag lift
2+0 992 19488 2.287080e-05 8.193038e-04 1.427359e+01 7.617550e-01
3+0 3968 76672 2.277423e-05 8.204231e-04 1.429177e+01 7.630484e-01
4+0 15872 304128 2.273175e-05 8.207084e-04 1.429484e+01 7.635608e-01
5+0 63488 1211392 2.271553e-05 8.208126e-04 1.429486e+01 7.636992e-01
6+0 253952 4835328 2.270838e-05 8.208548e-04 1.429451e+01 7.637359e-01
7+0 1015808 19320832 2.270493e-05 8.208773e-04 1.429426e+01 7.637460e-01

FSI2: x and y displacement of the point A
x and y displacement of A, ux zoom
x and y displacement of A, uy zoom)}}
FSI2: lift and drag force on the cylinder and flag
Lift on cylinder and flag
Drag on cylinder and flag

Results for FSI2 with timestep Δ=0.02
2+0 992 19488 -1.402e-2 ± 1.203e-2 [3.85] 1.25e-3 ± 7.93e-2 [1.93] 2.1010e+2 ± 7.262e+1 [3.85] 2.5e-1 ± 2.279e+2 [1.93]
3+0 3968 76672 -1.454e-2 ± 1.250e-2 [3.86] 1.25e-3 ± 8.07e-2 [1.93] 2.1306e+2 ± 7.576e+1 [3.86] 8.5e-1 ± 2.344e+2 [1.93]
4+0 15872 304128 -1.487e-2 ± 1.273e-2 [3.86] 1.24e-3 ± 8.17e-2 [1.93] 2.1283e+2 ± 7.589e+1 [3.86] 9.2e-1 ± 2.343e+2 [1.93]
Results for FSI2 with timestep Δ=0.01
level nel ndof ux(A) uy(A) drag lift
2+0 992 19488 -1.401e-2 ± 1.204e-2 [3.86] 1.25e-3 ± 7.93e-2 [1.93] 2.1009e+2 ± 7.282e+1 [3.86] 5.2e-1 ± 2.286e+2 [1.93]
3+0 3968 76672 -1.454e-2 ± 1.248e-2 [3.86] 1.25e-3 ± 8.07e-2 [1.93] 2.1306e+2 ± 7.576e+1 [3.86] 8.5e-1 ± 2.344e+2 [1.93]
4+0 15872 304128 -1.487e-2 ± 1.273e-2 [3.86] 1.24e-3 ± 8.17e-2 [1.93] 2.1518e+2 ± 7.778e+1 [3.86] 8.7e-1 ± 2.380e+2 [1.93]
Results for FSI2 with timestep Δ=0.0005
2+0 992 19488 -1.401e-2 ± 1.204e-2 [3.86] 1.28e-3 ± 7.92e-2 [1.93] 2.1014e+2 ± 7.286e+1 [3.86] 4.9e-1 ± 2.287e+2 [1.93]
3+0 3968 76672 -1.448e-2 ± 1.245e-2 [3.86] 1.24e-3 ± 8.07e-2 [1.93] 2.1305e+2 ± 7.574e+1 [3.86] 8.4e-1 ± 2.348e+2 [1.93]
4+0 15872 304128 -1.485e-2 ± 1.270e-2 [3.86] 1.30e-3 ± 8.16e-2 [1.93] 2.1506e+2 ± 7.765e+1 [3.86] 6.1e-1 ± 2.378e+2 [1.93]

FSI3: x and y displacement of the point A
x and y displacement of A, ux zoom
x and y displacement of A, uy zoom
FSI3: lift and drag force on the cylinder and flag
Lift on the cylinder and flag
Drag on the cylinder and flag

Results for FSI3 with timestep Δ=0.001
level nel ndof ux(A) uy(A) drag lift
2+0 992 19488 -3.02e-3 ± 2.83e-3 [10.75] 1.41e-3 ± 3.547e-2 [5.37] 4.582e+2 ± 2.832e+1 [10.75] 2.41 ± 1.4558e+2 [5.37]
3+0 3968 76672 -2.78e-3 ± 2.62e-3 [10.93] 1.44e-3 ± 3.436e-2 [5.46] 4.591e+2 ± 2.663e+1 [10.93] 2.41 ± 1.5126e+2 [5.46]
4+0 15872 304128 -2.86e-3 ± 2.70e-3 [10.95] 1.45e-3 ± 3.493e-2 [5.47] 4.602e+2 ± 2.765e+1 [10.95] 2.47 ± 1.5487e+2 [5.47]
Results for FSI3 with timestep Δ=0.0005
level nel ndof ux(A) uy(A) drag lift
2+0 992 19488 -3.02e-3 ± 2.85e-3 [10.75] 1.42e-3 ± 3.563e-2 [5.37] 4.587e+2 ± 2.878e+1 [10.75] 2.23 ± 1.4602e+2 [5.37]
3+0 3968 76672 -2.78e-3 ± 2.62e-3 [10.92] 1.44e-3 ± 3.435e-2 [5.46] 4.591e+2 ± 2.662e+1 [10.92] 2.39 ± 1.5068e+2 [5.46]
4+0 15872 304128 -2.86e-3 ± 2.70e-3 [10.92] 1.45e-3 ± 3.490e-2 [5.46] 4.602e+2 ± 2.747e+1 [10.92] 2.37 ± 1.5375e+2 [5.46]
Results for FSI3 with timestep Δ=0.00025
level nel ndof ux(A) uy(A) drag lift
2+0 992 19488 -3.02e-3 ± 2.85e-3 [10.74] 1.32e-3 ± 3.573e-2 [5.36] 4.587e+2 ± 2.880e+1 [10.74] 2.23 ± 1.4600e+2 [5.33]
3+0 3968 76672 -2.77e-3 ± 2.61e-3 [10.93] 1.43e-3 ± 3.443e-2 [5.46] 4.591e+2 ± 2.650e+1 [10.93] 2.36 ± 1.4991e+2 [5.46]
4+0 15872 304128 -2.88e-3 ± 2.72e-3 [10.93] 1.47e-3 ± 3.499e-2 [5.46] 4.605e+2 ± 2.774e+1 [10.93] 2.50 ± 1.5391e+2 [5.46]