calcCurvature

Overview

calcCurvature is a standalone application that builds the finite-area mesh (faMesh) of a case and evaluates the mean curvature of that surface for a single time. It writes two volume fields, curvature and curvatureNew. Both are zero everywhere except on the boundary patch named freeSurface or interface. The curvature it computes is the same faMesh::faceCurvatures() that capillaryInterface uses for the surface-tension pressure jump. Use it to check the curvature quality of a surface mesh (e.g. a spherical bubble, where $\kappa$ should be uniform) before running a capillary case. It is a single-mesh tool: it does not read multiRegionProperties and knows nothing about regions beyond the standard -region option.

Method

1. Time and mesh. The time is selected with the standard time options (see Usage). The run time is set to the first selected time, and only that time is processed. The mesh is created as a dynamicFvMesh (region from -region, default region0). If constant/[<region>/]dynamicMeshDict is absent, a staticFvMesh is used. The mesh is never moved.

2. Finite-area mesh. faMesh(mesh) is constructed for the default area name, i.e. it reads the faMesh written by makeFaMesh (constant/[<region>/]faMesh).

3. Patch detection. The boundary is scanned for a patch named freeSurface or interface. If both exist, the one with the higher patch index wins. If neither exists, the application aborts with a bare FatalError (no message).

4. Curvature (curvature). The faMesh face curvature is copied into the detected patch:

   $$ \mathbf{k}_N = \frac{1}{S_f}\sum_{e \in f} \mathbf{L}_e\, c_e, \qquad \kappa = \operatorname{sign}\!\left(\mathbf{k}_N\cdot\mathbf{n}_f\right)\,|\mathbf{k}_N| $$

   with $S_f$ the face area, $\mathbf{L}_e$ the edge length vectors (Le()), $c_e$ the edge length correction (edgeLengthCorrection(), $c_e = \cos\!\big(\tfrac{1}{2}\arcsin|\mathbf{n}_a\times\mathbf{n}_b|\big)$ from the two edge point normals) and $\mathbf{n}_f$ the faMesh face area normal. $\kappa$ is therefore signed relative to the faMesh normal.

5. Alternative curvature (curvatureNew). The same edge sum $\mathbf{k}_N$ is computed again. A unit “normal” is built from it, $\hat{\mathbf{n}} = \mathbf{k}_N/|\mathbf{k}_N|$, falling back to the fvPatch face normal where $|S_f\,\mathbf{k}_N| \le$ SMALL. The written value is

   $$ \kappa_\text{new} = \hat{\mathbf{n}}\cdot\mathbf{k}_N $$

   Because $\hat{\mathbf{n}}$ is parallel to $\mathbf{k}_N$, this is $|\mathbf{k}_N| = |\kappa|$ wherever the fallback is not active, i.e. the unsigned curvature.

6. Report. Min/max and arithmetic mean (unweighted by face area) of both patch fields are printed to the log.

Usage

Command line (standalone application):

calcCurvature [-region <name>] [-time <ranges> | -latestTime] [-constant] [-noZero]

Without time options all time directories (including 0/) are selected, so the earliest time is processed. If no time directory matches, constant/ is used with a warning.

Typical sequence for a single-mesh case:

blockMesh
makeFaMesh
calcCurvature

Input / Output

Read

Written to <time>/[<region>/] of the processed time:

All patches are of type calculated. No other fields are read or written.

Known Limitations

• Single time only. The selected time list is not looped over. Only the earliest selected time is processed, even if -time selects several.
• Fixed patch names. The patch must be called exactly freeSurface or interface. There is no option to pick another name (e.g. interfaceShadow). A missing patch aborts with an empty error message.
• faMesh must cover exactly that patch. The faMesh face values are assigned directly to the patch, so the faMesh must be built on that patch only, with the same face count and ordering. A faMesh on a different or additional patch causes a size mismatch.
• curvatureNew is unsigned. Its “normal” is derived from the edge sum itself rather than from the surface normal, so it carries no sign. It is not the signed normal force density that its comments suggest.
• Mean of face values. The printed average is an unweighted face average, not an area-weighted one.
• Libraries for the dynamicMeshDict. The application links only finiteVolume, finiteArea, dynamicFvMesh, dynamicMesh and meshTools. A dynamicMeshDict that selects a mesh type or motion solver from another library (e.g. interfaceTrackingFvMesh, or a motion solver from fvMotionSolvers) needs that library loaded through the dictionary’s library entries. Otherwise the selection fails.
• No parallel-specific handling. Min/max/average are evaluated per processor without reduction.

Tutorials