Modified stable methods and effect of artificial diffusion in the numerical study of viscoelastic fluid flow

Abstract

The trace of the polymer conformation tensor in numerical simulations is bounded by applying a logarithmic transformation to the elastic force in the finitely extensible nonlinear elastic-Peterlin model. This method, called elastic stress logarithmic transformation (EL), is combined with the artificial diffusion (AD) and square-root conformation reformulation (SRCR) methods to establish EL-AD and EL-SRCR methods, respectively. The accuracy and stability of these methods have been investigated by conducting direct numerical simulations of viscoelastic laminar flows around a circular cylinder at a Reynolds number Re = 100, considering a wide range of rheological parameters: the maximum polymer extensibility L = 10 and 100, and the Weissenberg number Wi=1−80. Specifically, effects of artificial diffusion coefficients measured by dimensionless Schmidt number Scc=10−106 on the flow are studied. The results indicate that the EL method can effectively ensure the boundedness and accuracy of the conformation tensor trace, making the EL-AD method a valuable modification of the AD method for simulations with larger L and Wi. The impact of the polymer stress diffusion on the simulation is complex. It can stabilize the simulation by reducing sharp gradients and peak positions of elastic stress. However, inappropriate artificial diffusion coefficients lead to flow artifacts when L is large (L = 100). One consequence is an amplification of the solid-like phenomenon caused by polymer near the upstream stagnation point of the cylinder. Another consequence is an enhanced suppression of vortices by polymer downstream of the cylinder. The challenge in determining a suitable AD coefficient emphasizes the superiority of the EL-SRCR method in terms of stability and accuracy.