## CSM tests

The structural tests are computed only for the elastic beam (without the surrounding fluid) adding the gravitational force only(!) on the structural part, $\vec{g}=(0,g)$ [ $\frac{\textrm{m}\nop}{\textrm{s}^2}$ ]. The CSM3 test is computed as a time dependent case starting from the undeformed configuration while the tests CSM1 and CSM2 are the steady state solutions.

Parameter settings for the CSM tests
par. dim. CSM1 CSM2 CSM3
$\varrho^s$ [ $10^3 \frac{\textrm{kg}\nop}{\textrm{m}^3}$ ] 1 1 1
$\nu^s$ 0.4 0.4 0.4
$\mu^s$ [ $10^6 \frac{\textrm{kg}\nop}{\textrm{ms}^2}$ ] 0.5 2.0 0.5
$\varrho^f$ [ $10^3 \frac{\textrm{kg}\nop}{\textrm{m}^3}$/span> ] 1 1 1
$\nu^f$ [ $10^{-3} \frac{\textrm{m}^2}{\textrm{s}\nop}$ ] 1 1 1
$\bar{U}$ [ $\frac{\textrm{m}\nop}{\textrm{s}\nop}$ ] 0 0 0
$g$ [ $\frac{\textrm{m}\nop}{\textrm{s}^2}$ ] 2 2 2
par. non-dim. CSM1 CSM2 CSM3
$\beta=\frac{\varrho^s}{\varrho^f}$ 1 1 1
$\nu^s$ 0.4 0.4 0.4
$\textrm{E}^s$ [ $\frac{\textrm{kg}\nop}{\textrm{ms}^2}$ ] 1.4 × 106 5.6 × 106 1.4 × 106
$\Re=\frac{\bar{U} d}{\nu^f}$ 0 0 0
$\bar{U}$ 0 0 0
$g$ 2 2 2

Results for CSM1
level nel ndof ux of A [ × 10-3] uy of A [ × 10-3 ]
2+0 320 6468 -7.17301 -66.0263
3+0 1280 25092 -7.18372 -66.0817
4+0 5120 98820 -7.18656 -66.0965
4+1 6260 120512 -7.18738 -66.1008
4+2 8552 164092 -7.18766 -66.1023
4+3 13148 251448 -7.18777 -66.1029
5+0 20480 392196 -7.18739 -66.1009
5+1 22772 435776 -7.18767 -66.1023

Results for CSM2
level nel ndof ux of A [ × 10-3] uy of A [ × 10-3 ]
2+0 320 6468 -0.468011 -16.9536
3+0 1280 25092 -0.468734 -16.9684
4+0 5120 98820 -0.468925 -16.9723
4+1 6260 120512 -0.468980 -16.9735
4+2 8552 164092 -0.468999 -16.9739
4+3 13148 251448 -0.469006 -16.9740
5+0 20480 392196 -0.468981 -16.9735
5+1 22772 435776 -0.469000 -16.9739

CMS3: The displacement of the point A

Results for CSM3 with timesteps $\Delta t=0.02, 0.01, 0.005$
level nel ndof ux of A [ × 10-3] uy of A [ × 10-3]
2+0 320 6468 -14.384 ± 14.389 [1.0956] -64.271 ± 64.595 [1.0956]
3+0 1280 25092 -14.402 ± 14.406 [1.0956] -64.352 ± 64.679 [1.0956]
4+0 5120 98820 -14.404 ± 14.408 [1.0956] -64.371 ± 64.695 [1.0956]
2+0 320 6468 -14.632 ± 14.636 [1.0978] -64.744 ± 64.907 [1.0978]
3+0 1280 25092 -14.645 ± 14.650 [1.0978] -64.765 ± 64.946 [1.0978]
4+0 5120 98820 -14.645 ± 14.650 [1.0978] -64.766 ± 64.948 [1.0978]
2+0 320 6468 -14.279 ± 14.280 [1.0995] -63.541 ± 65.094 [1.0995]
3+0 1280 25092 -14.299 ± 14.299 [1.0995] -63.594 ± 65.154 [1.0995]
4+0 5120 98820 -14.305 ± 14.305 [1.0995] -63.607 ± 65.160 [1.0995]