Sub-cell approximations for viscoelastic flows-filament stretching

Both fe- and fv-spatial discretisations are embedded within this methodology. Linear interpolation for stress, of either fe- or fv-form on triangular sub-cells, is referenced within parent triangular finite elements in two dimensions. Finite element discretisation is employed for the momentum and continuity system, via a second-order pressure-correction scheme. In this regard, a complex filament-stretching flow with a free-surface is selected to compute the transient evolution of kinematic and stress fields. Shortcomings of various upwinding schemes are discussed, whilst dealing with such free-surface type problems and appropriate strategies for dealing with these types of problems are outlined.