EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Issue ESAIM: M2AN
Volume 43, Number 6, November-December 2009
Page(s) 1117 - 1156
DOI 10.1051/m2an/2009034
Published online 01 August 2009

ESAIM: M2AN 43 (2009) 1117-1156
DOI: 10.1051/m2an/2009034

A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model

David J. Knezevic and Endre Süli

OUCL, University of Oxford, Parks Road, Oxford, OX1 3QD, UK. davek@comlab.ox.ac.uk; endre.suli@comlab.ox.ac.uk

Received October 23, 2008. Revised March 17, 2009. Published online August 1st, 2009.

Abstract
We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for the Fokker–Planck equation in configuration space with a finite element method in physical space to obtain a scheme for the high-dimensional Fokker–Planck equation. Alternating-direction methods have been considered previously in the literature for this problem (e.g. in the work of Lozinski, Chauvière and collaborators [J. Non-Newtonian Fluid Mech. 122 (2004) 201–214; Comput. Fluids 33 (2004) 687–696; CRM Proc. Lect. Notes 41 (2007) 73–89; Ph.D. Thesis (2003); J. Computat. Phys. 189 (2003) 607–625]), but this approach has not previously been subject to rigorous numerical analysis. The numerical methods we develop are fully-practical, and we present a range of numerical results demonstrating their accuracy and efficiency. We also examine an advantageous superconvergence property related to the polymeric extra-stress tensor. The heterogeneous alternating-direction method is well suited to implementation on a parallel computer, and we exploit this fact to make large-scale computations feasible.


Mathematics Subject Classification. 65M70, 65M12, 35K20, 82C31, 82D60.

Key words: Multiscale modelling, kinetic models, dilute polymers, alternating-direction methods, spectral methods, finite element methods, high-performance computing.


© EDP Sciences, SMAI 2009


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.