Pseudospectral calculations of viscoelastic flow in a periodically constricted tube

Abstract

The numerical implementation and results of a full pseudospectral method applied to the solution of an axisymmetric steady-state viscoelastic flow problem — the flow through a periodically constricted tube — are discussed. The method involves a double series expansion of the variables in terms of Fourier functions (sin and cos) in the periodic (axial) direction and Chebychev polynomials in the radial one. Results obtained with the Oldroyd-B viscoelastic fluid model are compared against those calculated using mixed pseudospectral / finite difference formulations. When viscoelasticity is absent (Newtonian viscous flow) the full pseudospectral calculations are extremely accurate; the small amplitude perturbation solution can be reproduced up to six digits of accuracy. The computed results in the Newtonian limit converge exponentially fast with the number of modes involved in either the radial or the axial directions. Furthermore, the results are in excellent agreement with the predictions obtained using independent numerical techniques. However, the accuracy of the calculations decreases with increasing elasticity in the flow, to the point where it becomes inferior to the accuracy obtained by the mixed techniques involving similar or less computational effort. The latter methods are shown to be much more robust, their accuracy being only slightly affected with increasing elasticity in the flow.