A new discrete EVSS method for the viscoelastic flows

In this paper, we propose a new discrete elastic–viscous-split-stress (EVSS) method for the viscoelastic flows obeying an Oldroyd-B type constitutive equation. Supposing that the velocity and pressure are approximated by the Taylor–Hood elements, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the discrete EVSS method. Compared with the popular one, the new method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. Additionally, some numerical experiments are shown to verify its efficiency.