Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Efficient and Stable Spectral Element Methods for Viscoelastic Flows

Presented by Tim Phillips, Cardiff University

21 November 2008 14:15 in CG218

This talk will consider the modelling of complex fluids and numerical
methods for predicting their flow. Typically, mathematical models for
complex fluids involve a nonlinear relationship between the stress and
strain. The level of description of the model to be used in a particular
application is determined by the available computational resources. Both
macroscopic and microscopic models for viscoelastic fluids will be
described. The former class of models include differential and integral
constitutive relationships derived from continuum mechanics
considerations. The latter class of models include kinetic theory models
for polymer solutions and reptation theory models for polymer melts.

In this talk some of the difficulties and peculiarities associated with
the numerical prediction of flows of complex fluids will be highlighted
and discussed. Alongside the conservation equations of mass and momentum,
which serve to determine the velocity and pressure, an equation for the
stress is also required. In a macroscopic model the stress is determined
by solving a differential or integral constitutive equation. In a
microscopic model the stress may be determined either by solving the
Fokker-Planck equation or an equivalent stochastic differential equation.
The application of the spectral element method to some benchmark flow
problems in non-Newtonian fluid mechanics will be described and the
salient features of the schemes will be highlighted. The benchmark
problems considered are the flow past a cylinder and the flow between
eccentrically rotating cylinders.

Contact m.p.j.jensen@durham.ac.uk for more information