Most steady-state viscoelastic flow problems require an evolution scheme to converge. You should generally start with a low Weissenberg number, and gradually increment it within an evolution. Although the 4×4 element is robust enough to allow the calculation of viscoelastic flows at high Weissenberg numbers, in most situations the first evolution step should be made at of the order of 0.3 to 0.5. The viscoelastic character of the flow depends on both the relaxation time and the flow rate . An evolution strategy can therefore be applied to either one, with an increasing evolution function .

When an evolution strategy is used, the initial and final values for the evolution parameter are important data. Again, based on the values of and , the first nonlinear solution (evaluated at ) should be selected so that the initial value of is about 0.3 to 0.5. If the evolution scheme is applied to , the initial value of can be zero.

If the evolution scheme is applied to , a nonzero value for is required, in order to start with a nonzero velocity field. A nonzero starting value for is always required when moving boundaries are involved. The final value of should be selected appropriately for the flow problem being solved. See Evolution for complete details about using evolution.

For problems with viscous and wall friction heating, you can apply an evolution technique to the scaling factor for the viscous and wall friction heating terms. Applying an evolution function on this scaling factor allows you to gradually introduce viscous and wall friction heating (see Using Evolution in Heat Conduction and Nonisothermal Flow Calculations for details). You can also apply an evolution technique to the cause of the viscous and wall friction heating (for example, the inlet flow rate). Another approach is to relate the thermal conductivity to and evolve from the conduction-dominated heat transfer case to the convection-diffusion case.

More generally, nonisothermal flows of high-viscosity materials often involve multiple nonlinearities, which arise from viscous and wall friction heating, thermal convection, and the temperature dependence of the viscosity. These three sources of nonlinearities create a strong coupling between momentum and energy equations. Appropriate evolutions schemes can be applied separately, or you can use a single menu item in the Numerical parameters menu to automatically set up all three evolution functions (as described in Using Evolution in Heat Conduction and Nonisothermal Flow Calculations).

In some circumstances, selecting an appropriate evolution strategy for solving a viscoelastic flow can be straightforward. However, there are situations where this is less obvious.

As with all nonlinear problems, you may encounter some convergence difficulties. For viscoelasticity flows, these difficulties often originate from the combination of high stress values developing in the vicinity of geometric singularities and of transport mechanisms inherent to viscoelasticity.

You can try to improve the solver behavior by applying evolution as part of your viscoelastic simulation. An easy way to do this is available for tasks defined as Steady or Evolution problem(s): simply click Enable convergence strategy for viscoelasticity in the Numerical parameters menu. Note that the current task will then be converted into an evolution task if it was previously defined as a steady task.

When this option is activated, viscoelasticity is progressively introduced into the system of equations being solved over the course of multiple evolution steps. This is done by progressively incorporating the constitutive modes into the solver and by progressively increasing the corresponding relaxation times. In other words, this is done in such a way that the actual important viscoelastic properties (namely viscosity and first normal stress difference) are progressively introduced into the calculation. If the final value of the evolution parameter is reached, then all required viscoelastic contributions are indeed incorporated into the simulation. If the final value of the evolution parameter could not be reached, then only a part of the selected viscoelastic model will actually be incorporated into the simulation. In general, the part of the rheological model relevant for high shear rates will be incorporated.

It is important to note that the convergence strategy for viscoelasticity takes care of the viscoelastic component of the simulation case only. In other words, it can be a good idea to make sure that the corresponding Newtonian calculation converges. This is also true when a simulation involves moving boundaries, since swelling for a viscoelastic flow is often more important than its Newtonian counterpart. The aim of the convergence strategy is to facilitate the start of the calculation, and in no way will it guarantee that a solution will be obtained for every case. While this convergence strategy is expected to lead to a solution in most cases, it by no means provides the optimum solution settings in terms of solution speed. It might be possible to find other solution setups which are computationally more effective.

Viscoelastic flows are sometimes defined in a more general context involving free surfaces and/or heat transport. When this is the case, it is quite natural to combine the convergence strategy for viscoelasticity with the convergence strategy for thermal flows and with evolution on moving boundaries. In many circumstances this will be sufficient; and in particular convergence for thermal flows can often with confidence be combined with convergence strategy for viscoelasticity.

When convergence strategy for viscoelasticity is enabled, care must sometimes be taken for free surface flows involving a pulling component, such as take-up velocity, take-up force or gravity. An additional evolution must sometimes be defined on the take-up velocity, which should preferably increase from the natural exit velocity to the desired one. Alternatively, an evolution can be defined on the take-up force or on the gravity, which starts from zero, however it should sometimes be invoked later in the calculation.

Despite these recommendations, there are simulation cases where the solver will fail. When this happens, the setup should anyway be checked and perhaps simplified. Sometimes however, another methodology may be needed, and which requires careful intervention from the user. Here, a sounded methodology may consist of two successive calculations. (i) In a first calculation, full slipping is asked while convergence strategy for viscoelasticity and evolution on moving boundaries are enabled. (ii) Upon completion of the first calculation, a second setup is defined which starts from the results of the first calculation, and for which convergence strategy for viscoelasticity and evolution on moving boundaries are disabled, while evolution is defined for the slipping law.

Consider a viscoelastic flow characterized by a typical shear rate s^-1 and a flow rate cm³/s. From viscometric data, the relaxation time is 0.1 s. Thus, .

The procedure for applying an evolution scheme to the flow rate is as follows. To start the calculations, the initial value of should be lower than 0.3. The initial flow rate should be specified so that the corresponding shear rate is about 3 s^-1. should therefore be set so that cm³/s. In the frame of the evolution strategy, Ansys Polyflow will increase the flow rate from the initial value up to the final value.

A more complex situation may occur for a White-Metzner model using a Bird-Carreau law with a low power-law index for the shear viscosity (see Theory and Equations). In this case, the initial flow rate must meet two criteria: the initial value of must be lower than 0.3 and the initial characteristic shear rate must be located in the plateau zone of the viscosity curve ().

For such complex problems, the evolution strategy can be applied simultaneously on different parameters (relaxation time, power-law index, and so on) with different evolution functions . Still, the easiest approach involves applying the evolution strategy only on the flow rate . Indeed, a low flow rate leads to a weakly nonlinear problem, while, from a physical viewpoint, the evolution strategy applies on the flow rate rather than on the fluid model itself.