Numerical simulation of flow of a polymer solution for Kolmogorov flow

A numerical method for approximating the equations of dynamics of a polymer solution flow is proposed. The proposed technique 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 using the linearized Godunov method. The polymer component of the flow is described by a system of equations for the polymer stretching vector $\mathbf{R}$ and is numerically approximated by the Kurganov–Tadmor method. Using this scheme, stability of the polymer solution flow at low Reynolds numbers $\mathrm{Re}\sim$ 10 in a square 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 is studied by means of a numerical experiment. The spectral characteristics of the polymer solution at low Reynolds numbers are constructed.