On Nov 14, 2007 12:36 PM, Dr Gerard Gorman <[EMAIL PROTECTED]> wrote:
> Hi
>
> On Wed, 2007-11-14 at 16:37 +0530, Prabhu Ramachandran wrote:
> > Thats the information available in the VTK class. The implementation is
> > here:
> >
> >
> http://public.kitware.com/cgi-bin/cvsweb.cgi/VTK/Graphics/vtkCellDataToPointData.cxx
> >
> > Basically, they find all the cells that share particular point. Then the
> > value at the point is the average of the values at the cells that share
> > the point. The weights are the same for all cells.
> >
>
> Eek - that doesn't look right. They should be using a finite element
> type projection method. ie - it should be something like (I hope you
> read latex)
> \begin{equation}
> field_n = (sum_e^{elements surrounding node n} field_e*volume_e)/
> (sum_e^{elements surrounding node n}volume_e)
> \end{equation}
> I'm using "element" and "cell" interchangeably here. If you don't do
> this then the result will be very inaccurate for inhomogeneous meshes.
>
> Cheers
> g
>
>
>
This interpolation scheme is also not good enough. It is not even exact for
a linear function, except when the vertex lies at the geometric centroid of
the surrounding elements. This shows up badly when the elements are
anisotropic; when you plot the contours of vertex values you can visually
make out that the interpolation is not accurate. In some finite volume
schemes, you need to interpolate to vertices from cell centroids. There,
people have used a "laplacian averaging" method which is exact for linear
functions, see for example
N. T. Frink, "Recent progress toward a three-dimensional unstructured
Navier-Stokes flow solver", AIAA-94-0061, 1994.
Or you could interpolate by least squares fitting of some polynomial.
praveen
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