## Curvature tests
### Files
* _curvature_test_data.csv_  
    Contains the data for all test numerical curvature models.

### Explanation of column names
The first five columns denote a parameter vector uniquely identifying a single curvature test.
* __numerical-curvature-model__: the four different curvature models reported in the paper. The mapping
    is as follows:
    * divGradMarkerField: DG$(\alpha)$
    * divGradSignedDistance: DG$(\phi)$
    * compactDivGradNoCorrection: cDG$(\phi)$
    * compactDivGradSphere: sccDG$(\phi)$
* __front-surface__: interface shape and configuration,
    * sphere: sphere of radius $R=1$
    * ellipsoid: ellipsoid with semi-axes $\mathbf{s} = [1.5, 1.0, 0.5]$
* __use-front-signed-distance__:
    * on: compute signed distance from triangulated surface
    * off: set signed distance analytically (exact)
* __resolution__: $n \in [16, 32, 64 ,128]$ cells in each spatial direction
* __step__: ID for each numerical test with randomized placement of interface centre. Runs from
    0 to 19 as each setup has been repeated 20 times.

The remaining columns contain metrics corresponding to the parameter vector of the row.
* __face L-inf-norm__: $L_\infty$-norm of relative curvature errors evaluated at cell faces.
* __face L2-norm__: $L_2$-norm of realtive curvature errors evaluated at cell faces.
* __face L1-norm__: $L_1$-norm of relative curvature errors evaluated at cell faces.
* __L-inf-norm__: $L_\infty$-norm of relative curvature errors evaluated at cell centres.
* __L2-norm__: $L_2$-norm of relative curvature errors evaluated at cell centres.
* __L1-norm__: $L_1$-norm of relative curvature errors evaluated at cell centres.
* __min-numerical__: minimum value of numerically approximated curvature. 
* __max-numerical__: maximum value of numerically approximated curvature.
* __min-exact__: minimum value of exact curvature.
* __max-exact__: maximum value of exact curvature.
* __t-exec__: approximate required execution time for the numerical curvature model given in
    microseconds.

### Used for:
The following plots and tables have been generated with the data from this csv file:
* Figure 6: scatter plot of $L_2$ curvature errors using the _face L2-norm_ values.
    (label: fig:curvature-l2-comparison)
* Table 2: Mean $L_\infty$ and $L_2$ norms of the relative curvature error and order
    of convergence for exact signed distance. Data from columns _face L-inf-norm_ and
    _face L2-norm_ has been used. (label: tab:curvature-errors-exact-distance)
* Table 2: Mean $L_\infty$ and $L_2$ norms of the relative curvature error and order
    of convergence for signed distance computed from the front. Data from columns
    _face L-inf-norm_ and _face L2-norm_ has been used.
    (label: tab:curvature-errors-front-distance)

## Stationary droplet
### Files and for what tables/figures they are used for
* _referenceData_stationaryDroplet_exactCurvaturePISO.csv_  
    Data for the Lent configuration from the first paper [(DOI)](https://doi.org/10.1016/j.compfluid.2014.12.019)
    prescribing a exact, constant curvature. Used for the following tables/figures:
    * Figure 10: temporal evolution of $L_\infty(|\mathbf{v}|)$ using the PISO algorithm
        (label: fig:sd-exact-curvature-piso)
    * Table 5: comparison between PISO and SAAMPLE (label: tab:sd-exact-curvature)
* _referenceData_stationaryDroplet_popinet2009.csv_  
    Data for the Lent configuration from the first paper (see DOI above), using an adopted setup
    from [Popinet (2009)](https://doi.org/10.1016/j.jcp.2009.04.042) with numerically approximated
    curvature. Used for the following tables/figures:
    * Figure 12 (label: fig:stationary-droplet-linf-comparison)
* _saamplePaperConfig_stationaryDroplet_exactCurvatureSAAMPLE.csv_  
    Data for the Lent configuration of the SAAMPLE paper prescribing exact, constant curvature.
    Used for the following tables/figures:
    * Table 5: comparison between PISO and SAAMPLE (label: tab:sd-exact-curvature)
* _saamplePaperConfig_stationaryDroplet_popinet2009.csv_  
    Data for the Lent configuration of the SAAMPLE paper, using an adopted setup
    from [Popinet (2009)](https://doi.org/10.1016/j.jcp.2009.04.042) with numerically approximated
    curvature.
    Used for the following tables/figures:
    * Figure 12 (label: fig:stationary-droplet-linf-comparison) 

### Explanation of column names
Parameter vector columns:
* __resolution__: equivalent resolution of the test case in each spatial direction
* __nu_droplet__: the kinematic viscosity used for the droplet and the ambient fluid
* __step__: index of the corresponding time step

Metric columns:
* __capillary number (whole domain)__: capillary number (eq. 37 / eq:capillary-number) computed with the maximum velocity in the entire domain
* __front volume__: volume enclosed by the front. Assumes the interface to be convex.
* __partial pressure error__: partial pressure error as defined in [Francois et al.(2006)](https://doi.org/10.1016/j.jcp.2005.08.004)
* __max delta P error__: maximum pressure difference error as defined in [Francois et al.(2006)](https://doi.org/10.1016/j.jcp.2005.08.004)
* __total pressure error__: total pressure error as defined in [Francois et al.(2006)](https://doi.org/10.1016/j.jcp.2005.08.004)
* __Linf droplet velocity error__: $L_\infty(|\mathbf{v}|)$ considering only the droplet phase
* __h__: the minimum distance between two cell centres. Corresponds to the mesh spacing for hexahedral meshes.
* __L1 velocity error__: $L_1(|\mathbf{v}|)$ considering the whole domain
* __time__: physical time in seconds
* __capillary number (droplet)__: capillary number (eq. 37 / eq:capillary-number) computed with the maximum velocity in the droplet phase
* __density ratio__: ratio of droplet density to ambient density: $\rho_d/\rho_a$
* __L2 velocity error__: $L_2(|\mathbf{v}|)$ considering the whole domain
* __Max mag(U) cell ID__: ID of the cell where $L_\infty(|\mathbf{v}|)$ is located
* __Linf velocity error__: $L_\infty(|\mathbf{v}|)$ considering the whole domain
* __centre-of-mass-x__: x-component of the centre of gravity
* __centre-of-mass-y__: y-component of the centre of gravity
* __centre-of-mass-z__: z-component of the centre of gravity
    

## Oscillating droplet
### Files and for what tables/figures they are used for
* _referenceData_oscillatingDroplet_shinJuric2011.csv_  
    Data for the Lent configuration from the first paper [(DOI)](https://doi.org/10.1016/j.compfluid.2014.12.019)
    adopting the setup from [Shin et al. (2011)](https://doi.org/10.1016/j.jcp.2011.04.040).
    Used for:
    * Figure 14 (label: fig:oscillating-droplet-semiaxis-evolution)
* _saamplePaperConfig_oscillatingDroplet_shinJuric2011.csv_  
    Data for the Lent configuration of the SAAMPLE paper.
    Used for:
    * Figure 14 (label: fig:oscillating-droplet-semiaxis-evolution)

### Explanation of column names
Parameter vector columns:
* __resolution__: equivalent resolution of the test case in each spatial direction
* __nu_droplet__: the kinematic viscosity set for the droplet phase
* __step__: index of the corresponding time step

Metric columns:
* __total_energy__: sum of kinetic and surface energy of the droplet
* __surface_energy__: surface energy of the droplet
* __time__: physical simulation time in seconds
* __kinetic_energy__: kinetic energy of the droplet phase
* __semi-axes-x__: length of the x-semi-axis
* __semi-axes-y__: length of the y-semi-axis
* __semi-axes-z__: length of the z-semi-axis
* __centre-of-mass-x__: x-component of the centre of gravity
* __centre-of-mass-y__: y-component of the centre of gravity
* __centre-of-mass-z__: z-component of the centre of gravity

## Translating droplet
### Files and for what tables/figures they are used for
* _referenceData_translatingDroplet_popinet2009.csv_
    Data for the Lent configuration from the first paper (see DOI above), using an adopted setup
    from [Popinet (2009)](https://doi.org/10.1016/j.jcp.2009.04.042) with numerically approximated
    curvature. Used for the following tables/figures:
    * Figure 13 (label: fig:translating-droplet-linf-comparison)
* _saamplePaperConfig_translatingDroplet_popinet2009.csv_
    Data for the Lent configuration of the SAAMPLE paper, using an adopted setup
    from [Popinet (2009)](https://doi.org/10.1016/j.jcp.2009.04.042) with numerically approximated
    curvature.
    Used for the following tables/figures:
    * Figure 13 (label: fig:translating-droplet-linf-comparison)

### Explanation of column names
Both parameter vector columns as well as metric columns are identical to the stationary droplet.
For all metrics which involve the computation of a norm of the velocity field, these computations
operate on the computed velocity field minus the background velocity, e.g.
$L_\infty(|\mathbf{v} - \mathbf{v}_{bg}|)$.
