A fully coupled high‐order discontinuous Galerkin solver for viscoelastic fluid flow

Abstract A fully coupled high order discontinuous Galerkin (DG) solver for viscoelastic Oldroyd B fluid flow problems is presented. Contrary to known methods combining DG the discretization of convective terms material model with standard finite element (FEM) and using elastic viscous stress splitting (EVSS) its derivatives, a local (LDG) formulation first described hyperbolic convection‐diffusion used. The overall scheme described, including temporal spatial as well solution strategies nonlinear system, based on incremental increase Weissenberg number. solvers suitability demonstrated two‐dimensional confined cylinder benchmark problem. immersed in narrow channel blocking ratio 1:2 drag force compared results from literature. Furthermore, steady unsteady calculations give brief insight into characteristics instabilities due boundary layer phenomena caused by viscoelasticity arising narrowing between cylinder.