Dilute polymer solutions: theory and simulation

• Date: 30. 11. 2017
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Hana Mizerová & Bangwei She (MÚ AV ČR, Praha)

Abstract: We propose a kinetic dumbbell-based model for dilute polymer solutions. The unsteady motion of the Newtonian solvent is described by the incompressible Navier-Stokes equations, while the Fokker-Planck equation describes the evolution of the probability density function of polymer molecules. Applying the Peterlin approximation to the nonlinear spring law, we derive a high-dimensional Navier-Stokes-Fokker-Planck system. We also have to deal with a problem of unbounded domain due to the infinite configuration space.  We show the existence of global in time weak solutions to the so-called kinetic Peterlin model and discuss its macroscopic closure. Further, we propose a multiscale scheme that is a combination of a stabilized Lagrange-Galerkin method and a Hermite spectral method. To our best knowledge, this is the first numerical simulation of kinetic models of viscoelastic fluids with infinitely extensible polymers.