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

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 6, page 1117-1156
- ISSN: 0764-583X

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topKnezevic, David J., and Süli, Endre. "A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1117-1156. <http://eudml.org/doc/250613>.

@article{Knezevic2009,

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. Fluids33 (2004) 687–696; CRM Proc. Lect. Notes41 (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.
},

author = {Knezevic, David J., Süli, Endre},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multiscale modelling; kinetic models; dilute polymers; alternating-direction methods; spectral methods; finite element methods; high-performance computing.; multiscale modelling; high-performance computing},

language = {eng},

month = {8},

number = {6},

pages = {1117-1156},

publisher = {EDP Sciences},

title = {A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model},

url = {http://eudml.org/doc/250613},

volume = {43},

year = {2009},

}

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: Mathematical Modelling and Numerical Analysis

DA - 2009/8//

PB - EDP Sciences

VL - 43

IS - 6

SP - 1117

EP - 1156

AB -
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. Fluids33 (2004) 687–696; CRM Proc. Lect. Notes41 (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.

LA - eng

KW - Multiscale modelling; kinetic models; dilute polymers; alternating-direction methods; spectral methods; finite element methods; high-performance computing.; multiscale modelling; high-performance computing

UR - http://eudml.org/doc/250613

ER -

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## Citations in EuDML Documents

top- John W. Barrett, Endre Süli, Finite element approximation of kinetic dilute polymer models with microscopic cut-off
- John W. Barrett, Endre Süli, Finite element approximation of kinetic dilute polymer models with microscopic cut-off
- John W. Barrett, Endre Süli, Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers
- John W. Barrett, Endre Süli, Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers

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