## CFD tests

Taking the flag as a rigid object, we perform 3 subtests focusing on the fluid dynamics part of the problem. The flag can be made almost rigid by setting the structural parameters to large values ($\varrho^s=10^6\frac{\textrm{kg}\nop}{\textrm{m}^3}$, $\mu^s=10^{12}\frac{\textrm{kg}}{\textrm{ms}^2}$) or completely rigid by considering the flow domain only with fixed boundary conditions on the flag interface.

Parameter settings for the CFD tests
dimensional parameter CFD1 CFD2 CFD3
$\varrho^f$ [ $10^3 \frac{\textrm{kg}\nop}{\textrm{m}^3}$/span> ] 1 1 1
$\nu^f$ [ $10^{-3} \frac{\textrm{m}^2}{\textrm{s}\nop}$ ] 1 1 1
$U$ [$\frac{m}{s}$] 0.2 1 2

Parameter settings for the CFD tests
non-dimensional parameter CFD1 CFD2 CFD3
$\Re=\frac{\bar{U} d}{\nu^f}$ 20 100 200
$\bar{U}$ [$\frac{\textrm{m}\nop}{\textrm{s}\nop}$] 0.2 1 2

Results for CFD1
level nel ndof drag lift
0+0 144 3032 1.41635 × 10+01 1.15592 × 10+00
1+0 576 11536 1.42236 × 10+01 1.11747 × 10+00
2+0 2304 44960 1.42730 × 10+01 1.11692 × 10+00
3+0 9216 177472 1.42880 × 10+01 1.11852 × 10+00
4+0 36864 705152 1.42919 × 10+01 1.11896 × 10+00
5+0 147456 2811136 1.42927 × 10+01 1.11904 × 10+00
5+1 150528 2869504 1.42929 × 10+01 1.11906 × 10+00
5+2 156672 2986240 1.42929 × 10+01 1.11905 × 10+00
5+3 168960 3219712 1.42929 × 10+01 1.11905 × 10+00
6+0 589824 11225600 1.42929 × 10+01 1.11905 × 10+00

Results for CFD2
level nel ndof drag lift
0+0 144 3032 1.33188 × 10+02 1.18522 × 10+01
1+0 576 11536 1.34996 × 10+02 1.10739 × 10+01
2+0 2304 44960 1.36355 × 10+02 1.05337 × 10+01
3+0 9216 177472 1.36610 × 10+02 1.05303 × 10+01
4+0 36864 705152 1.36678 × 10+02 1.05347 × 10+01
5+0 147456 2811136 1.36696 × 10+02 1.05349 × 10+01
5+1 150528 2869504 1.36700 × 10+02 1.05346 × 10+01
5+2 156672 2986240 1.36701 × 10+02 1.05343 × 10+01
5+3 168960 3219712 1.36701 × 10+02 1.05340 × 10+01
6+0 589824 11225600 1.36700 × 10+02 1.05343 × 10+01

CFD3: lift and drag forces on the cylinder and flag

Results for CFD3
levelnelndofdraglift
$\Delta t=0.01$
1+0 576 11536 416.8 ± 3.3578 [4.3825] -24.702 ± 342.38 [4.3825]
2+0 2304 44960 437.29 ± 5.3462 [4.3825] -11.085 ± 429.88 [4.3825]
3+0 9216 177472 438.99 ± 5.4419 [4.3825] -10.289 ± 433.09 [4.3825]
4+0 36864 705152 439.38 ± 5.4639 [4.3825] -9.9868 ± 434.79 [4.3825]
$\Delta t=0.005$
1+0 576 11536 416.83 ± 3.4023 [4.3956] -23.897 ± 346.72 [4.3956]
2+0 2304 44960 437.41 ± 5.5856 [4.3956] -12.673 ± 434.74 [4.3956]
3+0 9216 177472 439.05 ± 5.5804 [4.3956] -11.837 ± 436.17 [4.3956]
4+0 36864 705152 439.45 ± 5.6183 [4.3956] -11.893 ± 437.81 [4.3956]