Numerical simulation of viscoelastic fluid flows using a robust FVM framework on triangular grid

This paper presents a robust finite volume method (FVM) framework on unstructured triangular grid for simulating the viscoelastic flow of Oldroyd-B fluid. In order to enhance the numerical stability at high Weissenberg numbers, the framework adopts the CUBISTA scheme and the flux-based finite volume scheme to implement the spatial discretization of the Oldroyd-B constitutive equations, and the third order TVD Runge-Kutta method to perform the temporal discretization. Meanwhile, we use the cell centered FVM to discretize the conservation equations of mass and momentum, and the IDEAL algorithm to solve the discrete equations for the sake of robustness and efficiency. The validity of the presented FVM framework is testified by comparing the numerical results with the analytical solutions for the simple two-dimensional (2D) channel flow. In addition, we also simulate two more complex viscoelastic problems, i.e., the 2D lid-driven cavity flow and the 2D abrupt 4:1 planar contraction flow. The calculated results demonstrate that our method has a good numerical stability and works well for simulating viscoelastic fluid flows at moderately high values of Weissenberg number. (C) 2016 Elsevier B.V. All rights reserved.