In POLYDATA - How can I define a periodic boundary conditions based on flow rate for viscoelastic flow?

This can be done by editing the data file.

Remove the SOLVER defined for the calculation of inflow boundary conditions, and add a problem '53' (2D) or '54' (3D) to the main solver. That problems '53' and '54' are the same as for Newtonian calculations, and calculate a pressure gradient associated to the equation of flow rate.
A typical structure of that problem '53' is

#
BEGIN PROB1 13
# One problem specifications
. 1 0
C 16| Inflow
I 3| 53 1 3
I 2| 1 7
I 2| 2 9
I 2| 0 2
L 1| F
I 2| 5 0
D 0|
ENDOF PROB1

A similar concept is applied in 3D; the problem '54' is invoked.





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