Abstract
Non-Newtonian models with shear-thinning viscosity are commonly used to solve a variety of complex flow problems. A new finite-volume discretization based upon an unstructured grid is used to integrate the differential form of the lattice Boltzmann equation with a shear-dependent viscosity, using a cell-vertex finite-volume technique. The unknown fields are placed at the nodes of the mesh and evolve on the basis of the fluxes crossing the surfaces of the corresponding control volumes. Numerical results show a satisfactory accuracy also in the case of relatively complex geometries and demonstrate the ability of the method to predict the main features of non-Newtonian flows in straight and stenosed channels.