Numerical simulation of polymer solution flow for Kolmogorov flow

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Abstract

A numerical method approximating the equations of the dynamics of the polymer solution flow is proposed. The developed methodology is based on a hybrid approach. The hydrodynamic component of the flow is described by a system of Navier–Stokes equations and is numerically approximated by the linearized Godunov method. The polymer component of the flow is described by a system of equations for the polymer stretching vector R and is numerically approximated by the Kurganov–Tadmor method. Using the constructed scheme, the problem of the stability of the polymer solution flow at low Reynolds numbers Re ∼ 10 in a square periodic cell under the action of an external periodic force is investigated. The instability of this type of flow, characterized by a violation of its laminarity, has been studied by numerical experiment. Spectral characteristics of the polymer solution at low Reynolds numbers are constructed.

About the authors

V. V Denisenko

Institute of Design Automation of the Russian Academy of Sciences

Email: ned13@rambler.ru
Moscow, Russia

S. V Fortova

Institute of Design Automation of the Russian Academy of Sciences

Moscow, Russia

V. V Lebedev

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

V. V Kolokolov

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

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