Dr Gabriel Barrenechea, University of Strathclyde

Abstract: We propose a finite element discretisation of a three-dimensional non-Newtonian flow whose dynamics are described by an Upper Convected Maxwell model.

First, a one-directional simplification of the UCM problem is made, so the main

variables are velocity, pressure, and one vector which acts as the “square root”

of the stress tensor. For this model a finite element method is proposed and analysed.

The scheme preserves structure in the sense that the velocity is divergence-free and the overall discretisation is energy consistent with the underlying

problem. We investigate the problem’s complexity and devise relevant timestepping strategies for effcient solution realisation. We showcase the method with several numerical experiments, confirm the theory and demonstrate the efficiency of the scheme.