A stabilised finite element framework for viscoelastic multiphase flows using a conservative level-set method

Abstract

The development of stable numerical schemes for viscoelastic multiphase flows has implications for many areas of engineering applications. The principal original contribution of this paper is the implementation of a conservative level-set method to define implicitly the interface between fluid phases, fully integrated into the mathematical framework of viscoelastic flow. The governing equations are discretized using the finite element method and stabilisation of the constitutive equation is achieved using either the discontinuous Galerkin (DG) or streamline upwinding (SU) method. The discrete elastic viscous stress splitting gradient (DEVSS-G) formulation is also employed in the Navier-Stokes equations to balance the hyperbolic characteristics of the polymeric stress tensor. The numerical scheme is validated with reference to several benchmark problems and excellent quantitative agreement with published data is found for Newtonian and viscoelastic fluids, for both single and multiphase flows. The motion of a gas bubble rising in a viscoelastic fluid is studied in detail. The influence of polymer concentration, surface tension, fluid elasticity and shear-thinning behaviour, on flow features such as the development of filaments and cusps and the generation of negative wakes is explored.