Abstract:

Computational fluid dynamics (CFD) is a field in which
researchers and engineers predict the motion of a fluid using
computer simulations.  Water and Glycerin are examples of
fluids which are considered as Newtonian fluids, in which the
forces acting on a fluid element depend linearly on the rate of
deformation exhibited by the instantaneous flow (viscosity).
The equations that govern the dynamics of such fluids are known
as the Navier-Stokes equations. Simulations of such fluids are
widely performed both at the academia and the industry.

Polymer solutions, molten plastics, printing inks and blood
behave differently. In their case, the forces that govern the
flow are more complicated: they depend non-linearly on the
entire history of the deformation experienced by the fluid.
Such fluids are known as Visco-Elastic fluids and there are
several mathematical models used to describing their dynamics.
Although large amount of work has been devoted for the
development of computational methods to solve these equations,
they all suffer from a limiting critical elasticity value (the
Weissenberg number) above which the simulations break down.
This problem, commonly known as the "High Weissenberg Number
Problem", has been a major obstacle for the rheology community
for almost three decades. In this talk, we present a simple
analysis explaining the source of this breakdown. Based on this
observation, we propose a practical solution that stabilises
most of the existing methods.

This is a joint work with Prof. Raz Kupferman from the
Mathematics department at the hebrew university.