Lattice Boltzmann method for the simulation of the steady flow of a Bingham fluid in a pipe of square cross-section

In this paper, a simulation of the steady flow in a pipe of square cross-section has been performed when the pipe is filled with a Bingham fluid. The problem has been solved employing the Bingham model without any regularisation. An innovative approach based on a modification of the Lattice Boltzmann Method (LBM) has been applied to solve the problem. Yield stress effects on momentum transport using the Bingham model are investigated for certain pertinent parameters of the Oldroyd number, Od = 0.1-0.53 , and the hydraulic diameter, D_H = 1 and 2.