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