POLYFLOW - convergence/divergence, accuracy, precision for a power law or Bird-Carreau fluid model with a low index (non-Newtonian inelastic or generalised Newtonian)

Flow simulations that have a generalised Newtonian (non-Newtonian inelastic) fluid model, such as power law or Bird-Carreau, with a low power-law index may quickly diverge. What can be done to improve the success of these calculations?
For a shear-rate-dependent viscosity, POLYFLOW uses Newton iterations to compute the viscosity from the local shear rate, which is the default option.
For power-law or Bird-Carreau fluids with a low power index, Picard (fixed-point) iteration is recommended when evolution is not activated. The Picard scheme typically requires 20 to 30 iterations to converge to a tolerance of 1e-04, while the Newton scheme often requires 4 to 5 iterations. However, the radius of convergence for the Newton scheme is smaller for power-law fluids with a low index, i.e. a better initial solution guess is needed to ensure convergence. The Picard scheme provides better convergence behaviour when the power-law index is low.
For power-law or Bird-Carreau fluids with a low power-law index, the default Newton iteration can be used in combination with an evolution scheme that gradually decreases the power-law index. See Section 10.3.3 in the User's manual for details.

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