Adaptive high-order prediction of the drag correction factor for the upper-convected Maxwell fluid

An adaptive high-order finite element method is used to calculate the flow of a viscoelastic fluid around a sphere falling in a cylinder. No corner singularity appears in such a flow, but from a quite complex flow field, one predicts the drag correction factor for the upper-convected Maxwell fluid (UCM). Those properties explain why this problem is used as an benchmark for numerical techniques in rheology. Accuracy and robustness of the results are demonstrated by p-convergence analysis and by comparison with reference results. Hence, our calculations with high-order interpolations may be considered as reference results for this problem. The Galerkin and the Petrov-Galerkin techniques applied to several formulations (MIX, EVSS, AVSS) are analysed and compared. Error estimation and adaptivity allows us to derive optimal discretizations for each formulation. We observe that both suitable formulation and discretization are critical to obtain a valid prediction. (C) 1997 Elsevier Science B.V.