Numerical analysis of viscoelastic flow through a sinusoidally corrugated tube using a boundary element method

The flow of a viscoelastic fluid through a corrugated tube is important both for modeling the flow of polymeric fluids through porous media and for testing numerical methods in non‐Newtonian fluid mechanics. In this paper the boundary element method is used to solve this flow problem for various geometries. Newtonian, Maxwell, Oldroyd‐B, and modified Phan‐Thien–Tanner (MPTT) constitutive equations were used. The periodicity of the flow was guaranteed by treating the periodic conditions as parts of the system of equations. The effect of mesh refinement was considered and in some cases this was found to be negligible. The results are generally in good agreement with other investigators up to a Weissenberg number of about 6. After this point no convergence was reached with the present discretization. For the Maxwell and Oldroyd‐B fluids, the change in the flow resistance is small (∼5% decrease) as the Weissenberg number increases. An increase in the flow resistance with the Weissenberg number was observed in the MPTT fluid when the rheological parameter ζ≠0.