  In this paper, the performance of two lattice Boltzmann method formulations
for yield-stress (i.e. viscoplastic) fluids has been investigated. The first
approach is based on the popular Papanastasiou regularisation of the fluid
rheology in conjunction with explicit modification of the lattice Boltzmann
relaxation rate. The second approach uses a locally-implicit formulation to
simultaneously solve for the fluid stress and the underlying particle
distribution functions. After investigating issues related to the lattice
symmetry and non-hydrodynamic Burnett stresses, the two models were compared in
terms of spatial convergence and their behaviour in transient and inertial
flows. The choice of lattice and the presence of Burnett stresses was found to
influence the results of both models, however the latter did not significantly
degrade the velocity field. Using Bingham flows in ducts and synthetic porous
media, it was found that the implicitly-regularised model was superior in
capturing transient and inertial fluid behaviour. This result presents
potential implications for the application of the Papanastasiou-regularised
model in such scenarios. In creeping flows the performance of both models was
found to be both similar and satisfactory.
