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We study an ad hoc extension of the Lattice-Boltzmann method that allows thesimulation of non-Newtonian fluids described by generalized Newtonian models.We extensively test the accuracy of the method for the case of shear-thinningand shear-thickening truncated power-law fluids in the parallel plate geometry,and show that the relative error compared to analytical solutions decaysapproximately linear with the lattice resolution. Finally, we also tested themethod in the reentrant-flow geometry, in which the shear-rate is no-longer ascalar and the presence of two singular points requires high accuracy in orderto obtain satisfactory resolution in the local stress near these points. Inthis geometry, we also found excellent agreement with the solutions obtained bystandard finite-element methods, and the agreement improves with higher latticeresolution

Lattice Boltzmann method for non-Newtonian (power-law) fluids