Simulation of Die-swell Flow for Oldroyd-B Model with Feedback Semi-implicit Taylor Galerkin Finite Element Method

This work is focused on creeping die-swell flow for Oldroyd-B fluid in two-dimensional axisymmetric system. The governing equations are solved via a combination of semi-implicit Taylor-Galerkin/pressure-correction finite element method and feedback condition. Some extra techniques for local velocity gradient recovery scheme and streamline-upwind/Petrov-Galerkin method are employed to improve the stability of solutions. For each time step after velocity field is computed, the specific region of die swell jet is adjusted while finite triangle elements in this area are re-meshed. Finally, the benchmark of swelling ratio with other literatures and analytical theory is presented in positive direction.