  We propose a Finite Volume Method for the simulation of elastoviscoplastic
flows, modelled after the extension to the Herschel-Bulkley model by Saramito
[J. Non-Newton. Fluid Mech. 158 (2009) 154-161]. The method is akin to methods
for viscoelastic flows. It is applicable to cell-centred grids, both structured
and unstructured, and includes a novel pressure stabilisation technique of the
"momentum interpolation" type. Stabilisation of the velocity and stresses is
achieved through a "both sides diffusion" technique and the CUBISTA convection
scheme, respectively. A second-order accurate temporal discretisation scheme
with adaptive time step is employed. The method is used to obtain benchmark
results of lid-driven cavity flow, with the model parameters chosen so as to
represent Carbopol. The results are compared against those obtained with the
classic Herschel-Bulkley model. Simulations are performed for various lid
velocities, with slip and no-slip boundary conditions, and with different
initial conditions for stress. Furthermore, we investigate the cessation of the
flow, once the lid is suddenly halted.
