We show how to transform a large class of differential constitutive models into an equation for the (matrix) logarithm of the conformation tensor. Under this transformation, the extensional components of the deformation field act additively, rather than multiplicatively. This transformation is motivated by numerical evidence that the high Weissenberg number problem may be caused by the failure of polynomial-based approximations to properly represent exponential profiles developed by the conformation tensor. The potential merits of the new formulation are demonstrated for a finitely-extensible fluid in a two-dimensional lid-driven cavity at Weissenberg number Wi = 5.
Bibliographical noteFunding Information:
We are grateful to Alexandre Chorin, Erez Lapid and Lior Silberman for useful advice. This research was funded and supported in part by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the US Department of Energy under Contract DE-AC03-76-SF00098.
- Finite differences
- High Weissenberg number problem