Numerical simulation of elastic turbulence in a confined two-dimensional cell

A numerical model that approximates the system of equations of a viscous fluid with the use of polymeric molecules is described. This model is hybrid and is based on the application of Godunov linearized and finite-difference schemes. This scheme is used to calculate a Kolmogorov-type problem - a viscous flow in a confined area (a square cell) under the action of an external periodic force. The flow with and without impurity is compared, the behavior of polymer molecules in different flow regions is studied. A transition regime characterized by almost complete stretching of molecules in regions of high velocity gradient is obtained.