K. K. Wang

VISCOELASTIC MODELLING OF ENTRANCE FLOW USING MULTIMODE LEONOV MODEL

A simulation of planar 2D flow of a viscoelastic fluid employing the Leonov constitutive equation has been presented. Triangular finite elements with lower-order interpolations have been employed for velocity and pressure as well as the extra stress tensor arising from the constitutive equation. A generalized Lesaint-Raviart method has been used for an upwind discretization of the material derivative of the extra stress tensor in the constitutive equation. The upwind scheme has been further strengthened in our code by also introducing a non-consistent streamline upwind Petrov-Galerkin method to modify the weighting function of the material derivative term in the variational form of the constitutive equation. A variational equation for configurational incompressibility of the Leonov model has also been satisfied explicitly. The corresponding software has been used to simulate planar 2D entrance flow for a 4:1 abrupt contraction up to a Deborah number of 670 (Weissenberg number of 6.71) for a rubber compound using a three-mode Leonov model.

Everywhere-G 2 -continuous interpolation with C 2 Gregory patches

In some engineering applications, G2 continuity of free-form surfaces is very important. C2 Gregory patch has been introduced to generate G2 continuous surfaces and a method was developed to connect two C2 Gregory patches with G2 continuity. However, since C2 Gregory patch has such a singularity that neither its second partial derivatives nor curvature can be generally decided at its corner points, the method could not guarantee G2 continuity there. In this paper we have developed a new method that removes the singularity and generates everywhere-G2-continuous surfaces with C2 Gregory patches. We also discuss interpolations of non-rectangular faces by use of our method.