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Computation of free surface flows with a Taylor-Galerkin/pressure-correction algorithm

A semi-implicit Taylor-Galerkin/pressure-correction finite element scheme (STGFEM) is developed for problems that manifest free surfaces associated with the incompressible creeping flow of Newtonian fluids. Such problems include stick-slip and die-swell flows, both with and without a superimposed drag flow, and for plane, axisymmetric and annular systems. The numerical solutions are compared with available analytical and numerical solutions, both in the neighbourhood of singularities and elsewhere. Close correspondence in accuracy is extracted from the literature for both stick-slip and die-swell flows. Stick-slip flow is used as a precursor study to the more complex free surface calculations involved for die-swell in extrudate flow. Two different free surface techniques are reported and results are analysed with mesh refinement and varying structure