Here I propose an implicit strategy for power-law non-Newtonian fluids within the LB framework https://www.researchgate.net/publication/263746696_Harmonic_oscillations_of_laminae_in_non-Newtonian_fluids_a_lattice_Boltzmann-immersed_boundary_approach?ev=prf_pub

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Article Harmonic oscillations of laminae in non-Newtonian fluids: A ...

There are two main ways for doing this. One is to have a variable tau (relaxation time) which changes as a function of the shear stress (or appropriate variable) based on a non-Newtonian model such as the power law. This is done in [1] and [2]. The alternative is to use a 'body force' model such as the BG-CL model proposed in [3].

The key advantage of using the LBM is that the shear stress can be found locally without the need to calculate velocity gradients using equation (13) in [1] or equation(4) of [3]

[1] https://www.researchgate.net/publication/228631840_A_second-order_accurate_lattice_Boltzmann_non-Newtonian_flow_model

[2] https://www.researchgate.net/publication/253269711_Analysis_of_the_Casson_and_Carreau-Yasuda_non-Newtonian_blood_models_in_steady_and_oscillatory_flows_using_the_lattice_Boltzmann_method

[3] http://www.sciencedirect.com/science/article/pii/S037843711400692X#

Article A Second-Order Accurate Lattice Boltzmann Non-Newtonian Flow Model

Article Analysis of the Casson and Carreau-Yasuda non-Newtonian bloo...

Thank you a lot Buick and Rosis.

To have a LBE model for linear visco-elastic fluids (non-Newtonian), you can look at the paper by P. Lallemand et al. published in PRE (2003), and a recent paper by P. Dellar in SIAM J. Sci. Comput. (2014).  The older papers are by L. Giraud et al.

It is important to know exactly what "non-Newtonian" fluid means.