ON CONVERGENT SCHEMES FOR TWO-PHASE FLOW OF DILUTE POLYMERIC SOLUTIONS

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Metzger S
Zeitschrift: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique
Jahr der Veröffentlichung: 2019
Band: 52
Heftnummer: 6
Seitenbereich: 2357-2408
ISSN: 0764-583X


Abstract

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grun, Metzger, M3AS 26 (2016) 823-866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Metzger, Stefan Dr.
Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen)


Zitierweisen

APA:
Metzger, S. (2019). ON CONVERGENT SCHEMES FOR TWO-PHASE FLOW OF DILUTE POLYMERIC SOLUTIONS. Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 52(6), 2357-2408. https://dx.doi.org/10.1051/m2an/2018042

MLA:
Metzger, Stefan. "ON CONVERGENT SCHEMES FOR TWO-PHASE FLOW OF DILUTE POLYMERIC SOLUTIONS." Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique 52.6 (2019): 2357-2408.

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Zuletzt aktualisiert 2019-25-02 um 09:08