Abstract: Based on the log-conformation representation (LCR), we gave two fully coupled numerical methods  for viscoelastic Oldroyd-B flow problems, and conducted a comparative study on two methods. The first method was to introduce the discrete elastic-viscous split-stress gradient (DEVSS-G) method into the momentum equation, which enhanced the ellipticity of the momentum equation and obtained the LCR-DEVSS-G stabilization scheme. The second method was to combine the streamline upwind Petrov-Galerkin (SUPG) method, we obtained  the LCR-SUPG stabilization scheme. Finally, the verification results of numerical examples of Poiseuille flow and flow around a circular cylinder show  that using LCR-DEVSS-G stabilization scheme to handle viscoelastic Oldroyd-B flow problems has  better convergence and higher computational efficiency.

Key words: viscoelastic fluid, Oldroyd-B model, log-conformation-representation, discrete elastic-viscous split-stress gradient method, streamline upwind Petrov-Galerkin