On the simulation of a time‐dependent cavity flow of an Oldroyd‐B fluid

In this article we present a finite element method for simulating the time‐dependent flow of an Oldroyd‐B fluid in a lid‐driven cavity, which is a stringent test problem at high Weissenberg number. The key considerations for developing the methodology are the preservation of the positive definiteness of the conformation tensor via the log‐conformation representation and additional diffusion, from second‐order upwind scheme, to smooth the high‐frequency modes. The combination of the log‐conformation representation, finite element method, and an operator‐splitting Lie's scheme, gives us a robust and easy‐to‐implement scheme. We have obtained convergent results when simulating time‐dependent cavity flows.