Numerical approximation of corotational dumbbell models for dilute polymers
We construct a general family of Galerkin methods for the numerical approximation of weak solutions to a bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier-Stokes...
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| Format: | Journal article |
| Language: | English |
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2009
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| author | Barrett, J Sueli, E |
| author_facet | Barrett, J Sueli, E |
| author_sort | Barrett, J |
| collection | OXFORD |
| description | We construct a general family of Galerkin methods for the numerical approximation of weak solutions to a bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier-Stokes equations, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function satisfying a Fokker-Planck-type parabolic equation. We focus on finitely extensible nonlinear elastic-type dumbbell models. In the case of a corotational drag term, we perform a rigorous passage to the limit as the spatial and temporal discretization parameters tend to zero and show that a (sub)sequence of numerical solutions converges to a weak solution of this coupled Navier-Stokes-Fokker-Planck system. |
| first_indexed | 2024-03-07T05:34:46Z |
| format | Journal article |
| id | oxford-uuid:e3828089-9bf5-4ba7-8987-9023a583dfd9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:34:46Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:e3828089-9bf5-4ba7-8987-9023a583dfd92022-03-27T10:09:34ZNumerical approximation of corotational dumbbell models for dilute polymersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e3828089-9bf5-4ba7-8987-9023a583dfd9EnglishSymplectic Elements at Oxford2009Barrett, JSueli, EWe construct a general family of Galerkin methods for the numerical approximation of weak solutions to a bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier-Stokes equations, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function satisfying a Fokker-Planck-type parabolic equation. We focus on finitely extensible nonlinear elastic-type dumbbell models. In the case of a corotational drag term, we perform a rigorous passage to the limit as the spatial and temporal discretization parameters tend to zero and show that a (sub)sequence of numerical solutions converges to a weak solution of this coupled Navier-Stokes-Fokker-Planck system. |
| spellingShingle | Barrett, J Sueli, E Numerical approximation of corotational dumbbell models for dilute polymers |
| title | Numerical approximation of corotational dumbbell models for dilute polymers |
| title_full | Numerical approximation of corotational dumbbell models for dilute polymers |
| title_fullStr | Numerical approximation of corotational dumbbell models for dilute polymers |
| title_full_unstemmed | Numerical approximation of corotational dumbbell models for dilute polymers |
| title_short | Numerical approximation of corotational dumbbell models for dilute polymers |
| title_sort | numerical approximation of corotational dumbbell models for dilute polymers |
| work_keys_str_mv | AT barrettj numericalapproximationofcorotationaldumbbellmodelsfordilutepolymers AT suelie numericalapproximationofcorotationaldumbbellmodelsfordilutepolymers |