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 ( 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.
Mots clés : multiscale modelling, kinetic models, dilute polymers, alternating-direction methods, spectral methods, finite element methods, high-performance computing
@article{M2AN_2009__43_6_1117_0, author = {Knezevic, David J. and S\"uli, Endre}, title = {A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1117--1156}, publisher = {EDP-Sciences}, volume = {43}, number = {6}, year = {2009}, doi = {10.1051/m2an/2009034}, mrnumber = {2588435}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2009034/} }
TY - JOUR AU - Knezevic, David J. AU - Süli, Endre TI - A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 1117 EP - 1156 VL - 43 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009034/ DO - 10.1051/m2an/2009034 LA - en ID - M2AN_2009__43_6_1117_0 ER -
%0 Journal Article %A Knezevic, David J. %A Süli, Endre %T A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 1117-1156 %V 43 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009034/ %R 10.1051/m2an/2009034 %G en %F M2AN_2009__43_6_1117_0
Knezevic, David J.; Süli, Endre. A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 6, pp. 1117-1156. doi : 10.1051/m2an/2009034. http://www.numdam.org/articles/10.1051/m2an/2009034/
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