Numerical analysis of the transpose diffusive term for viscoplastic-type non-Newtonian fluid flows using a collocated variable arrangement

Abstract

The aim of this work is to delve into the numerical analysis of viscoplastic-type non-Newtonian fluid flows. Specifically, improvements in the spatial discretization schemes and the temporal integration methods have been proposed to overcome the numerical problems introduced by the transpose diffusive term and associated with the velocity field discontinuity, the artificial viscous diffusion, and the transpose viscous coupling. The resulting knowledge may be useful, among many other reasons, to improve the corresponding numerical simulations and gain insight into the underlying physics of this class of non-Newtonian fluid flows.

The aim of this work is to delve into the numerical analysis of viscoplastic-type non-Newtonian fluid flows. Specifically, improvements in the spatial discretization schemes and the temporal integration methods have been proposed to overcome the numerical problems introduced by the transpose diffusive term and associated with the velocity field discontinuity, the artificial viscous diffusion, and the transpose viscous coupling. The resulting knowledge may be useful, among many other reasons, to improve the corresponding numerical simulations and gain insight into the underlying physics of this class of non-Newtonian fluid flows.