Numerical study for solving plane Couette and plane Poiseuille flows of an Oldroyd fluid

Abstract

This work deals with the numerical solutions of viscoelastic fluid flow, this solutions corresponding to unsteady unidirectional flow of Oldryod fluids. Numerical solution is based on finite difference method using implicit Crank-Nicolson scheme for the velocity, and improved Euler method for the stress tensor. The numerical results of plane Couette flow and plane Poiseuille flow obtained by this method are presented and compared with the steady solution when time $t$ is large enough.