Abstract:
A numerical method is proposed that approximates the equations of the dynamics of a weakly compressible viscous flow in the presence of a polymer component of the flow. The behavior of the flow under the influence of a static external periodic force in a periodic square cell is investigated. The methodology is based on a hybrid approach. The hydrodynamics of the flow is described by a system of Navier – Stokes equations and is numerically approximated by the linearized Godunov method. The polymer field is described by a system of equations for the vector of stretching of polymer molecules R, which is numerically approximated by the Kurganov – Tedmor method. The choice of
model relationships in the development of a numerical methodology and the selection of modeling parameters made it possible to qualitatively model and study the regime of elastic turbulence at low Reynolds Re $\sim10^{-1}$. The polymer solution flow dynamics equations differ from the Newtonian fluid dynamics equations by the presence on the right side of the terms describing the forces acting on the polymer component part. The proportionality coefficient A for these terms characterizes the backward influence degree of the polymers number on the flow. The article examines in detail how the flow and its characteristics change depending on the given coefficient. It is shown that with its growth, the
flow becomes more chaotic. The flow energy spectra and the spectra of the polymers stretching field are constructed for different values of A. In the spectra, an inertial sub-range of the energy cascade is traced for the flow velocity with an indicator $k\sim-4$, for the cascade of polymer molecules stretches with an indicator $-1.6$.
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