One common observation in Non-Newtonian fluid mechanics is that
the numerical results deteriorate as the meshes refine. However,
in our integration scheme, we take the temporal
quadrature points to be dependent on the meshes. So as the mesh is refined,
the results are more accurate. The price to pay is much more
computation needed for this integration scheme. Nevertheless,
switching to a parallel environment lowers such a burden. For example,
for the 810 element case, it took about 20 hours to run a case on
an 8-node Intel system whereas it took more than 4 days on DEC-5000
and more than a week on Sun SPARC.
Without the capability of a parallel processor,
we would not have been able to verify our theories of numerical breakdown,
spurt phenomena and deterioration of results when the mesh is refined.
We hope to continue using the Intel supercomputers for further understanding
of industrially important polymeric fluids in the near future.