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.

Automated summary

This article presents two different artificial diffusion stabilization methods for numerical simulations of steady Oldroyd-B fluid flows. These methods are based on the idea of vanishing in time added stabilization terms, which are gradually eliminated during the time-marching process towards the steady state solution. These additional terms naturally disappear and do not affect the final result. The numerical simulations are performed on a simple steady 2D case of Oldroyd-B fluid flow in a symmetrical corrugated channel. The numerical solver uses finite element discretization in space and the 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 potential efficiency of the different stabilization techniques used.