A multigrid method for solving steady viscoelastic fluid flow Original Research Article

A numerical method is presented in order to analyze steady viscoelastic fluid flows. A finite difference technique has been introduced on a non-uniform staggered grid system by adopting an upwind scheme to discretize the constitutive equations where the stress tensor can be decomposed into Newtonian and non-Newtonian parts. In both, the FAS (Full Approximation Storage) multigrid algorithm is used. The performance of this method is investigated for the stick–slip and the four-to-one abrupt plane contraction problems. We have selected Oldroyd B and Phan Thien–Tanner fluid models for the calculations. Some results prove that the Oldroyd model is not totaly appropriate.