Abstract: 

A numerical technique is proposed for modeling the flow of viscous polymer solutions and studying the phenomenon of elastic turbulence. The method is a hybridization of the numerical methods of two-dimensional linearized Godunov scheme and the Kurganov-Tadmor method. Linearized Godunov scheme was used to approximate the hydrodynamic part of the equations of a polymer solution dynamics, and is a two-dimensional method of S.K. Godunov with linear discontinuity decays, which provides guaranteed non-decreasing entropy. The flow of a Kolmogorov type polymer solution in a periodic square cell, pumped by an external periodic force and characterized by the Reynolds number Re~10^-1, is investigated. The instability of the flow is obtained, the transition to the elastic turbulence regime is investigated. The spectral characteristics of the turbulent flow are constructed, and the power-law slope of the inertial interval is estimated.