  We present a methodology for simulating three-dimensional flow of
incompressible viscoplastic fluids modelled by generalised Newtonian
rheological equations. It is implemented in a highly efficient framework for
massively parallelisable computations on block-structured grids. In this
context, geometric features are handled by the embedded boundary approach,
which requires specialised treatment only in cells intersecting or adjacent to
the boundary. This constitutes the first published implementation of an
embedded boundary algorithm for simulating flow of viscoplastic fluids on
structured grids. The underlying algorithm employs a two-stage Runge-Kutta
method for temporal discretisation, in which viscous terms are treated
semi-implicitly and projection methods are utilised to enforce the
incompressibility constraint. We augment the embedded boundary algorithm to
deal with the variable apparent viscosity of the fluids. Since the viscosity
depends strongly on the strain rate tensor, special care has been taken to
approximate the components of the velocity gradients robustly near boundary
cells, both for viscous wall fluxes in cut cells and for updates of apparent
viscosity in cells adjacent to them. After performing convergence analysis and
validating the code against standard test cases, we present the first ever
fully three-dimensional simulations of creeping flow of Bingham plastics around
translating objects. Our results shed new light on the flow fields around these
objects.
