An efficient algorithm for strain history tracking in finite element computations of non‐Newtonian fluids with integral constitutive equations

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Abstract
A new finite element technique has been developed for employing integral‐type constitutive equations in non‐Newtonian flow simulations. The present method uses conventional quadrilateral elements for the interpolation of velocity components, so that it can conveniently handle viscoelastic flows with both open and closed streamlines (recirculating regions). A Picard iteration scheme with either flow rate or elasticity increment is used to treat the non‐Newtonian stresses as pseudo‐body forces, and an efficient and consistent predictor‐corrector scheme is adopted for both the particle‐tracking and strain tensor calculations. The new method has been used to simulate entry flows of polymer melts in circular abrupt contractions using the K‐BKZ integral constitutive model. Results are in very good agreement with existing numerical data. The important question of mesh refinement and convergence for integral models in complex flow at high flow rate has also been addressed, and satisfactory convergence and mesh‐independent results are obtained. In addition, the present method is relatively inexpensive and in the meantime can reach higher elasticity levels without numerical instability, compared with the best available similar calculations in the literature.