hp-adaptivity in finite element methods for viscoelastic flow simulation

Doctorat en sciences appliquées -- UCL, 199

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 theology. 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

Adaptive hp-finite element viscoelastic flow calculations

Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure