The simultaneous use of 4×4 and 2×2 bilinear stress elements for viscoelastic flows

Abstract

Mixed finite elements for viscoelastic flows based on a 4×4 sub-linear interpolation for the extra stress components satisfy the Babuska-Brezzi condition and are highly stable. They have been proved to be quite satisfactory in solving problems with strong stress boundary layers. In this work, we examine the simultaneous use of 4×4 and 2×2 bilinear stress elements in an attempt to reduce the computational cost without sacrificing the accuracy. The 4×4 bilinear elements are employed in regions where the stress field is anticipated to be steep while the 2×2 elements carry the burden elsewhere with a much smaller number of stress nodes. Additional constraints along the sides shared by different elements are necessary in order to preserve conformity. The method is applied to the creeping flow of a Maxwell fluid around a sphere falling along the axis of a cylindrical tube. Results are given for three mixed finite element formulations: the Galerkin method, the consistent streamline-upwind/Petrov-Galerkin method (SUPG) and the non-consistent streamline-upwind method (SU). Particular emphasis is given on the calculated drag correction factors. The effect of the sphere/cylinder diameter ratio is also examined. © 1993 Springer-Verlag.