  Subject of this paper is the derivation of a new constitutive law in terms of
the logarithm of the conformation tensor that can be used as a full substitute
for the 2D governing equations of the Oldroyd-B, Giesekus and other models. One
of the key features of these new equations is that - in contrast to the
original log-conf equations given by Fattal and Kupferman (2004) - these
constitutive equations combined with the Navier-Stokes equations constitute a
self-contained, non-iterative system of partial differential equations. In
addition to its potential as a fruitful source for understanding the
mathematical subtleties of the models from a new perspective, this analytical
description also allows us to fully utilize the Newton-Raphson algorithm in
numerical simulations, which by design should lead to reduced computational
effort. By means of the confined cylinder benchmark we will show that a finite
element discretization of these new equations delivers results of comparable
accuracy to known methods.
