POLYFLOW - a possible evolution for non-isothermal flow with viscous heating

What could be a convenient evolution scheme for non-isothermal flows involving viscous heating?
When viscous heating is incorporated into a flow calculation, a thermal capacity is needed for absorbing the heat generated. Hence, an increasing evolution scheme for the coefficient of heat capacity would not be allways appropriate here, even though it is known to be useful for convection dominated flows.
Instead, it can be a good idea to apply a decreasing evolution scheme on the thermal conductivity. By doing so, at the beginning of the calculation, the heat generated via viscous heating will be entirely absorbed and also largely diffused throughout the flow via conduction. Conduction will of course decrease when the coefficient of thermal conductivity decreases within the selected evolution scheme.

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