A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154-161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the momentum interpolation and both sides diffusion types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls.