Two:dimensional time-dependent calculations for a molecular model of f
inite extensibility in the journal-bearing geometry are presented. The
flow is considered to be incompressible and isothermal. The momentum
conservation equation is integrated using a time-marching procedure in
which local ensembles of dumbbells act as stress calculators. The cal
culations are based on the Calculation of non-Newtonian flows: finite
elements and stochastic simulation technique (CONNFFESSIT) and combine
deterministic (finite elements) and stochastic techniques to advance
the velocity and stress fields in time. The ability of CONNFFESSIT to
treat models for which no closed-form constitutive equation can be der
ived is illustrated by performing calculations using FENE dumbbells. S
ignificant differences in the stress field between the true FENE and t
he linearized FENE-P are found, especially during the inception period
Steady-state kinematics are, however identical within error bars for
both FENE and FENE-P and for the Newtonian fluid. The essential algori
thm of 2-D CONNFFESSIT is detailed, as well as experience gathered fro
m its parallel and vector versions.