A cell-based smoothed CBS finite element formulation for computing the Oldroyd-B fluid flow

In this paper, a cell-based smoothed finite element method (CS-FEM) incorporating characteristic-based split (CBS) scheme is developed to compute viscoelastic fluid flow. The system of the Navier-Stokes and Oldroyd-B constitutive equations is decoupled in tandem with equal low-order approximation of the triple primitive variables. The spatial discretization is based upon CS-FEM which readily smooths all gradient-related entries of the governing equations over bilinear four-node quadrilateral elements. Moreover, the cell-based smoothing concept is applied to evaluation of viscoelastic fluid force. Four benchmark problems are replicated to demonstrate the applicability and robustness of the smoothed CBS finite element formulation. A good agreement is exposed between the present and previous results.