THE RESEARCH PROGRESS OF LATTICE BOLTZMANN METHOD IN NON-NEWTONIAN FLUID FLOW

LBM (lattice Boltzmann method) allows straightforward calculations of the local shear rate to the second-order accuracy, so it has some advantages in the simulation of the non-Newtonian behavior of flows． Although the suitability of LBM for the non-Newtonian flow has been well demonstrated, the algorithms are mainly through instantaneously regulating the local relaxation time in the BGK (Bhatnagar-Gross-Krook) approximated collision term to match its corresponding viscosity for reflecting the effect of the local rheology variation．This approach, however, might cause some numerical instabilities when the relation time is close to 1/2．In this paper, the advances of LBM applied to generalized Newtonian flows are reviewed．The methods to mitigate numerical instabilities are described and the results are compared．Several ways of extending LBM to viscoelastic flows in the literature are introduced．Finally the prospective developments of LBM for non-Newtonian flows are suggested．