An efficient stabilized finite element scheme for simulating viscoelastic flows

Abstract

AbstractThis article presents an efficient stabilized finite element scheme for solving viscoelastic flow problems at high Weissenberg numbers. The velocity and pressure variables in the momentum balance equations are uncoupled using an incremental fractional step method based on the second‐order backward differentiation formula. The pressure gradient projection stabilization technique and the discrete elastic‐viscous‐split‐stress formulation are introduced into the scheme, in explicit versions, to circumvent the LBB constraints. For the constitutive equation, a square root transformation is first applied to preserve the positive definiteness of the polymer conformation tensor, and then the streamline upwind/Petrov–Galerkin method and the second‐order Runge–Kutta scheme are implemented for spatial and time discretizations. Three benchmark problems are tested and numerical results have revealed the accuracy and convergence of the scheme. What is more, since the presented scheme enables the use of equal low‐order interpolations for all variables, and requires no iterative process, it is computationally efficient and easy to be implemented.