CFD Utilities Files

SURFACE_CURVATURE Description:

   For a structured multiblock surface or volume grid, calculate four forms
of curvature and save the surface results in Tecplotable form.  If the grid
is a volume grid, determine the face of each block most likely to be a
solid wall (via the smallest average off-wall increment) and output results
for that face of the block.

   This version has the option to add unit surface normals to the output.

   The two main forms of curvature are Gaussian and mean curvature, from
which two principal curvatures can be derived.  Most of the calculations
are performed in subroutine "gaussian_curvature", q.v. for further details.

   Note that the partial derivatives of x, y, z with respect to arc length
along the grid lines are not true partial derivatives if the surface grid
lines are not orthogonal.  Thus, in general, these curvature results are
approximate only, less so the more orthogonal the surface grid lines.  A
hemispherical test case gives very good results on the three main patches
but the end cap patches that avoid singular points have almost 180-degree
interior angles.  The method breaks down at those corners (though it is
safeguarded), and is noisy near them.

   Another weakness is that there is no guarantee of continuity across
surface patches at common boundaries, since only one patch is treated at a
time, with one-sided differencing at grid line end points.

History:

   09/07/05  D. A. Saunders  Initial implementation, for CEV capsules.
   09/08/05     "     "      Added output of the principal curvatures.
   09/09/05     "     "      Handled volume grids as well as surface grids.
   09/12/05     "     "      More careful solution of the quadratic for the
                             principal curvatures.
   10/03/06     "     "      Installed Tecplot 360 version of the I/O pkg.
   11/27/07     "     "      A question from Todd White about surface
                             normals led to adding such an option here.

Author:  David Saunders, ELORET Corporation/NASA Ames Research Center, CA