Although the evolutive viscosity (see Numerical Method for Integral Viscoelastic Flow) has been introduced for numerical reasons only, it is recommended that you specify its value based on physical considerations. Two possibilities are available: constant and variable evolutive viscosity.

By default, the evolutive viscosity is a constant value computed from

(11–62)

where are the viscosities of the viscoelastic modes, as specified in each viscoelastic model. This evolutive viscosity is independent of the shear rate. If you prefer to specify a constant value explicitly, select Modification of the evolutive viscosity in the Evolutive Viscosity menu. (The default value is zero, which indicates that Equation 11–62 will be used to compute .) The recommended value is the zero-shear-rate viscosity.

You can also specify a variable evolutive viscosity, which is computed from

(11–63)

This evolutive viscosity exhibits the same shear-rate dependence as the integral fluid model itself.

To change to a variable evolutive viscosity, select Switch to Variable Evolutive Viscosity in the Evolutive Viscosity menu.

From a numerical point of view, the iterative scheme based on the constant evolutive viscosity seems to be more stable and is generally recommended. In some cases, however, constant-viscosity Newtonian solutions do not exist, but a solution can be found when the viscosity is shear-rate-dependent. This is the case for some problems with very large free-surface deformations (for example, film blowing dies).

If you use Equation 11–63 (variable evolutive viscosity), the system solved by Ansys Polyflow has the following form:

(11–64)

where and depend on the shear rate. This iterative scheme is less stable than if is constant. In order to avoid numerical instabilities, it is possible to keep the evolutive viscosity in matrix constant and limit the use of a variable evolutive viscosity to the right-hand side. Then the following system is solved instead:

(11–65)

Equation 11–65 will be solved by Ansys Polyflow if you use Equation 11–62 for a constant evolutive viscosity or specify your own constant value explicitly.

In all cases, both techniques are equivalent once . Using the technique of Equation 11–65, it is possible to start an integral evolution task from a generalized Newtonian solution.