Application of vanishing diffusion stabilization in Oldroyd-B fluid flow simulations

Two different methods of artificial diffusion stabilization of the numerical simulations of steady Oldroyd-B fluids flows are presented. They are based on the idea of vanishing in time added stabilization terms which are only present during the initial stage of time-marching process towards the steady state solution. These extra terms naturally vanish and do not affect the final result. The numerical simulations are built on a simple steady 2D case of Oldroyd-B fluid flow in a symmetrical corrugated channel. Numerical solver uses finite element discretization in space and characteristic Galerkin method for pseudo-time discretization. Numerical results are presented in the form of isolines and graphs of selected flow variables, to assess the possible efficiency of the different stabilization techniques used. Article Highlights New numerical algorithm for stabilization of Oldroyd-B fluids flows is proposed and tested. The vanishing artificial diffusion extends the range of stability of the given numerical method. The proposed numerical stabilization method is easy to implement into existing codes.