For problems with inertia, you can relate the density to the evolution parameter . The Reynolds number will thus be directly related to the evolution parameter.

For problems with a high Péclet number, you can relate the thermal conductivity to . When is small, is large, and the energy equation is diffusion-dominated. When increases, decreases, approaching the correct value. Note that in this case, the initial value of cannot be zero (the default value). Similarly, you can relate the heat capacity to and obtain the same effect.

Note that this technique may not be applicable for some problems involving strong viscous and wall friction heating dissipation.

For natural convection problems, you can relate the thermal expansion coefficient ( in Equation 13–9) or the gravity to the evolution parameter .

Nonisothermal flows can often benefit from the evolution technique. Nonisothermal flows of high-viscosity materials often involve multiple nonlinearities, which are simultaneous and have different origins. Typically, the nonlinearities 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 evolution 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).

If you are only concerned with viscous and wall friction heating, you can apply an evolution technique to the scaling factor for the viscous and wall friction heating term. 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.

Shear-thinning fluids are very good candidates for the evolution technique. Consider a power-law fluid, or any fluid that behaves like a power-law fluid in the actual range of shear rate. When the power-law index is low, it is generally impossible to obtain a converged solution with the Newton-Raphson method if you impose the actual value of from the start.

There are two remedies to this problem. You can use the Picard iteration for the viscosity instead of the Newton-Raphson iteration, as described in Viscosity-Related Iterations. An easy way to do this is available for tasks defined as Steady or Evolution problem(s): simply click Enable convergence strategy for rheology/slip in the Numerical parameters menu. Note that the current task will not be converted into an evolution task if it was defined as a steady task. This convergence strategy consists in using Picard iterations for viscosity and slipping. The other remedy is to associate with the evolution parameter , so that decreases as increases.

Successive calculations with decreasing values of , using Newton-Raphson iterations, provide a successful technique for calculating such complex flows.

Note that, for very low values of (0 to 0.2), it may still be necessary to use Picard iterations instead of Newton-Raphson iterations with evolution. Many iterations with the Picard scheme will be required to reach an appropriate level of convergence. With the Picard iteration, the convergence rate of the solver can be rather slow, especially with a low power index; and reaching a given relative convergence on the velocity does not necessarily guarantee an upper bound of the departure with respect to the actual solution. When using the Picard iteration, it is therefore suggested that you invoke a more severe relative convergence criterion on the velocity field, on the order of 10^-4 (or sometimes 10^-5).