
READ ME File For 'Dataset supporting the publication "The effect of variations in experimental and computational fidelity on data assimilation approaches"'

Dataset DOI: 10.5258/SOTON/D3137

Date that the file was created: 06/2024

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GENERAL INFORMATION
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ReadMe Author: Uttam Cadambi Padmanaban, University of Southampton

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SHARING/ACCESS INFORMATION
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Licenses/restrictions placed on the data, or limitations of reuse:

Recommended citation for the data:  Please use the above doi

This dataset supports the publication: 
AUTHORS: C. Thompson, U. Cadambi Padmanaban, B. Ganapathisubramani and S. Symon
TITLE: The effect of variations in experimental and computational fidelity on data assimilation approaches
JOURNAL: TCFD
PAPER DOI IF KNOWN: 10.1007/s00162-024-00708-y


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DATA & FILE OVERVIEW
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This dataset contains:


1. Fig2: This contains the psuedo-PIV data set for the three camera resolutions of 4MP, 8MP and 16MP.
The data is provided as a structured grid running from bottom left of the domain to the top right, row-wise.

FourMegapixXSampled - X co-ordinates of the cell-centroids of data points for the 4MP camera case.
FourMegapixYSampled - Y co-ordinates of the cell-centroids of data points for the 4MP camera case.
FourMegapixUmeanSampled - sampled streamwise velocity for the 4MP camera case.
FourMegapixVmeanSampled - sampled wall-normal velocity for the 4MP camera case.

EightMegapixXSampled - X co-ordinates of cell-centroids of the data points for the 8MP camera case.
EightMegapixYSampled - Y co-ordinates of cell-centroids of the data points for the 8MP camera case.
EightMegapixUmeanSampled - sampled streamwise velocity for the 8MP camera case.
EightMegapixVmeanSampled - sampled wall-normal velocity for the 8MP camera case.

SixteenMegapixXSampled - X co-ordinates of the cell-centroids of data points for the 16MP camera case.
SixteenMegapixYSampled - Y co-ordinates of the cell-centroids of data points for the 16MP camera case.
SixteenMegapixUmeanSampled - sampled streamwise velocity for the 16MP camera case.
SixteenMegapixVmeanSampled - sampled wall-normal velocity for the 16MP camera case.

2. Fig4: This contains the mean streamwise velocity field for the baseline case of highest computational resolution (21,600) and the assimilated fields from variational and state observer methods (for the highest camera resolution of 16MP) along with the u = 0 streamlines.

Column 1: X co-ordinates of the cell-centroids the data points.
Column 2: Y co-ordinates of the cell-centroids of the data points.
Column 3: mean streamwise velocity.

fig4_baseline_mean_fields.dat - baseline mean streamwise velocity data.
fig4_baseline_streamline.dat - dividing streamline for baseline case (u = 0).
fig4_variational_mean_fields.dat - varaiational data assimilated mean streamwise velocity field.
fig4_variational_streamline.dat - dividing streamlines for variational method (u = 0).
fig4_state_observer_mean_fields.dat - state observer data assimilated mean streamwise velocity field.
fig4_state_observer_streamline.dat - dividing streamlines for state observer method (u = 0).

3. Fig5: This contains the mean streamwise and wall normal velocity data for variatioanal and state observer methods at lowest computational mesh resolution (7200) and highest input data resolution (16MP camera). Note: for the streamwise mean velocity of the highest computational mesh resolution (21600) and highest input data resolution (16MP), please refer to data supplied in 2.

fig5_variational_7200.dat - variational data assimilated mean streamwise and wall normal velocity fields at lowest computational mesh resolution (7200) and highest input data resolution (16MP).
Column 1: X co-ordinates of the cell-centroids.
Column 2: Y co-ordinates of the cell-centroids.
Column 3: mean streamwise velocity.
Column 4: mean wall-normal velocity.

fig5_state_observer_7200.dat - state observer data assimilated mean streamwise and wall normal velocity fields at lowest computational mesh resolution (7200) and highest input data resolution (16MP).
Column 1: X co-ordinates of the cell-centroids.
Column 2: Y co-ordinates of the cell-centroids.
Column 3: mean streamwise velocity.
Column 4: mean wall-normal velocity.

fig5_variational_21600_Uy.dat - variational data assimilated mean wall normal velocity field for highest computational mesh (21600) and input data (16MP) resolutions.
Column 1: X co-ordinates of the cell-centroids.
Column 2: Y co-ordinates of the cell-centroids.
Column 3: mean wall-normal velocity.

fig5_state_observer_21600_Uy.dat - state observer data assimilated mean wall normal velocity field for highest computational mesh (21600) and input data (16MP) resolutions.
Column 1: X co-ordinates of the cell-centroids.
Column 2: Y co-ordinates of the cell-centroids.
Column 3: mean wall-normal velocity.

4. Fig6: This contains the mean streamwise velocity profiles at different streamwise stations at the highest (4MP) and lowest(16MP) input data resolutions and the highest computational mesh resolution (21600). 

Each file has a common string "Centerline" followed by a number starting from 1 to 9. 
Centerline_U.xy: x/H = 1.
Centerline1_U.xy: x/H = 2.
Centerline2_U.xy: x/H = 3.
Centerline3_U.xy: x/H = 4.
Centerline4_U.xy: x/H = 5.
Centerline5_U.xy: x/H = 6.
Centerline6_U.xy: x/H = 7.
Centerline7_U.xy: x/H = 8.
Centerline8_U.xy: x/H = 9.

The rest of the file name corresponds to either variational or state observer methods at either 4MP or 16MP resolutions.

Column 1: Y co-ordinates of the cell-centroids sampled along a vertical line from the bottom to the top wall at the cell-centroids.
Column 2: mean streamwise velocity sampled at the Y co-ordinates in column 1.
Column 3: mean wall-normal velocity sampled at the Y co-ordinates in column 1.
Column 4: mean spanwise velocity sampled at the Y co-ordinates in column 1.

5. Fig8: this contains the skin-friction coefficient (Cf) and the wall pressure gradient (dCp/dx) for the variational and state observer methods compared with the baseline simulations at their respective mesh resolutions at the lowest (4MP and 7200) and highest (16MP and 21,600) input data and computational mesh resolutions respectively.


fig8_baseline_7200_dcpdx.dat - baseline mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations.

fig8_baseline_21600_dcpdx.dat - baseline mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations.

fig8_variational_7200_dcpdx.dat - variational data assimilated mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200) and the lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations for a 4MP camera resolution.
Column 3: dCpdx at these locations for a 16MP camera resolution.

fig8_variational_21600_dcpdx.dat - variational data assimilated mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600) and the lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations for a 4MP camera resolution.
Column 3: dCpdx at these locations for a 16MP camera resolution.

fig8_state_observer_7200_dcpdx.dat- state observer data assimilated mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200) and the lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations for a 4MP camera resolution.
Column 3: dCpdx at these locations for a 16MP camera resolution.

fig8_state_observer_21600_dcpdx.dat - state observer data assimilated mean pressure gradient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600) and the lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: dCpdx at these locations for a 4MP camera resolution.
Column 3: dCpdx at these locations for a 16MP camera resolution.

fig8_baseline_7200_cf.dat - baseline mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations.

fig8_baseline_21600_cf.dat - baseline mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations.

fig8_variational_7200_cf.dat - variational data assimilated mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200) and the lowest and highest input data resolutions (4MP and 16MP).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations for a 4MP camera resolution.
Column 3: cf at these locations for a 16MP camera resolution.

fig8_variational_21600_cf.dat - variational data assimilated mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600) and the lowest and highest input data resolutions (4MP and 16MP).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations for a 4MP camera resolution.
Column 3: cf at these locations for a 16MP camera resolution.

fig8_state_observer_7200_cf.dat - state observer data assimilated mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the lowest computational mesh resolution (7200) and the lowest and highest input data resolutions (4MP and 16MP).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations for a 4MP camera resolution.
Column 3: cf at these locations for a 16MP camera resolution.

fig8_state_observer_21600_cf.dat - state observer data assimilated mean skin-friction coefficient along the bottom wall sampled at the centres of the bottom patch for the highest computational mesh resolution (21600) and the lowest and highest input data resolutions (4MP and 16MP).

Column 1: X coordinates of the centres of the cells along the bottom patch.
Column 2: cf at these locations for a 4MP camera resolution.
Column 3: cf at these locations for a 16MP camera resolution.

6. Fig9: this contains the curl of the forcing term comparing the DNS case with the variational and state observer data assimilated cases at highest and lowest computational mesh and input data resolutions respectively (4MP and 16MP, 7200 and 21600).  

fig9_dns_curl_f.dat - curl of the forcing term obtained from DNS.
Column 1: X coordinates of the cell-centroids.
Column 2: Y coordinates of the cell-centroids.
Column 3: curl of the forcing.

fig9_variational_7200_curl_f.dat - curl of the forcing term for variational data assimilated case of lowest computational mesh resolution (7200) and lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the cell-centroids.
Column 2: Y coordinates of the cell-centroids.
Column 3: curl of forcing for 4MP case.
Column 4: curl of forcing for 16MP case.

fig9_variational_21600_curl_f.dat - curl of the forcing term for variational data assimilated case of highest computational mesh resolution (21600) and lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the cell-centroids.
Column 2: Y coordinates of the cell-centroids.
Column 3: curl of forcing for 4MP case.
Column 4: curl of forcing for 16MP case.

fig9_state_observer_7200_curl_f.dat - curl of the forcing term for state observer data assimilated case of lowest computational mesh resolution (7200) and lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the cell-centroids.
Column 2: Y coordinates of the cell-centroids.
Column 3: curl of forcing for 4MP case.
Column 4: curl of forcing for 16MP case.

fig9_state_observer_21600_curl_f.dat - curl of the forcing term for state observer data assimilated case of highest computational mesh resolution (21600) and lowest and highest input data resolutions (4MP and 16MP).
Column 1: X coordinates of the cell-centroids.
Column 2: Y coordinates of the cell-centroids.
Column 3: curl of forcing for 4MP case.
Column 4: curl of forcing for 16MP case.

7. Fig11: this contains the hyperparameter study of Kp for the state observer method showing the rate of convergence of the L1 norm for different values of Kp.

fig11_L1_mean_list_M4.dat - L1 norm, Kp = 10^-4.
fig11_L1_mean_list_M5.dat - L1 norm, Kp = 10^-5.
fig11_L1_mean_list_M6.dat - L1 norm, Kp = 10^-6.
fig11_L1_mean_list_M7.dat - L1 norm, Kp = 10^-7.

8. Fig12: computational cost of lowest and highest computational mesh and camera resolutions (7200 and 21600, 4MP and 16MP) for the variational and state observer methods. 

Column 1: number of primal solver calls.
Column 2: L1/max(L1).

fig12_variational_4MP_7200.dat: variational method, 4MP input data resolution, 7200 mesh resolution.
fig12_variational_16MP_21600.dat: variational method, 16MP input data resolution, 21600 mesh resolution.
fig12_state_observer_4MP_7200.dat: state observer method, 4MP input data resolution, 7200 mesh resolution.
fig12_state_observer_16MP_21600.dat: state observer method, 16MP input data resolution, 21600 mesh resolution.











