  We investigate the elastoviscoplastic flow through porous media by numerical
simulations. We solve the Navier-Stokes equations combined with the
elastoviscoplastic model proposed by Saramito for the stress tensor evolution.
In this model, the material behaves as a viscoelastic solid when unyielded, and
as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress.
The porous media is made of a symmetric array of cylinders, and we solve the
flow in one periodic cell. We find that the solution is time-dependent even at
low Reynolds numbers as we observe oscillations in time of the unyielded region
especially at high Bingham numbers. The volume of the unyielded region slightly
decreases with the Reynolds number and strongly increases with the Bingham
number; up to 70% of the total volume is unyielded for the highest Bingham
numbers considered here. The flow is mainly shear dominated in the yielded
region, while shear and elongational flow are equally distributed in the
unyielded region. We compute the relation between the pressure drop and the
flow rate in the porous medium and present an empirical closure as function of
the Bingham and Reynolds numbers. The apparent permeability, normalized with
the case of Newtonian fluids, is shown to be greater than 1 at low Bingham
numbers, corresponding to lower pressure drops due to the flow elasticity, and
smaller than 1 for high Bingham numbers, indicating larger dissipation in the
flow owing to the presence of the yielded regions. Finally we investigate the
effect of the Weissenberg number on the distribution of the unyielded regions
and on the pressure gradient.
