The modeling of surface tension forces is computationally difficult because it requires the evaluation of surface curvatures, i.e., second derivatives of the surface location. This is
particularly true in FLOW-3D® since it uses a regular rectangular grid that does not conform to surface shapes. Although this simple grid structure makes it more difficult to evaluate surface
slopes and curvatures, it is this feature that also gives the strength needed to simulate coalescence and breakup of fluid blobs.
Evaluation of surface slope and curvature in FLOW-3D® is done by determining which coordinate direction is closest to the outward normal vector to the surface. Then fluid in a 3 by 3
by 3 set of grid cells surrounding a given cell is summed up in the cell columns parallel to the normal. This, in effect, gives a discrete representation of the surface height in nine (3×3)
columns, which can be used to compute slopes and curvatures.
In most cases this procedure works quite well, but when normal directions in the grid are near 45° the surface may be too steep for this procedure to work accurately. A consequence of this
loss of accuracy is the introduction of spurious pressures or perturbations that sometimes generate undesirable capillary waves (i.e., kinetic energy noise). Occasionally, these
perturbations can even destroy a computation.
A summary of the original surface tension model was given in Technical Note TN6, “Surface Tension Validation Tests,” (1987). Since that Note there have been a number of major improvements:

1. Wall adhesion sensitive to slope of wall,
2. Static contact angle as an obstacle property,
3. Two-fluid interfacial surface tension,
4. Thermocapillary (i.e., tangential) surface forces (see TN47).

In this Technical Note we document another improvement that has been made. In particular, we have improved the accuracy of the column summation technique for the computation of surface
curvatures. As the following examples will show, this improvement is quite dramatic in many cases where the earlier model experienced substantial difficulties.