Numerical Investigation of Two-Dimensional Oldroyd-B Fluid Flows Over A Straight Rectangular Domain

In this paper, non-Newtonian viscoelastic Oldroyd-B fluid flows in two-dimensional rectangular domain is numerically investigated, where the flow between two rigid walls is driven by a pressure difference along -direction (horizontal). The numerical results of the nonlinear system of partial differential equations are obtained by decoupling the system into Navier-Stokes system and tensorial transport equation. Computational Fluid Dynamics (CFD) simulations are done by using the finite element method. The numerical simulations are presented in terms of the contours of velocity, pressure and extra stress tensor. The Hood-Taylor finite element method is used for the approximation of the velocity and the pressure while the discontinuous Galerkin method is used to approximate the stress tensor. All the meshes and simulations are carried out by the general finite element solver FreeFem++, which has been found as a potential tool to provide a reasonably good numerical simulations of complicated flow behavior.