A HETEROGENEOUS ALTERNATING-DIRECTION METHOD FOR A MICRO-MACRO DILUTE POLYMERIC FLUID MODEL

Journal article

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. © 2009 EDP Sciences SMAI.

Authors: Knezevic, D; Sueli, E

• Publication status: Published
• Journal: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
• Volume: 43
• Issue: 6
• Pages: 1117-1156
• Publication date: 2009-01-01
• DOI: 10.1051/m2an/2009034
• EISSN: 1290-3841
• ISSN: 0764-583X
• Language: English
• Keywords: alternating-direction methods; spectral methods; kinetic models; finite element methods; Multiscale modelling; high-performance computing; dilute polymers