This article is cited in 1 paper

Collection of papers in honor of Sergey Godunov (Editors: Yu. L. Trakhinin, M.A. Shishlenin)

Application of a two-dimensional version of the linearized Godunov scheme to the numerical simulation of the Kolmogorov problem for a liquid polymer solution

V. V. Denisenko, S. V. Fortova

Institute for Computer Aided Design of the Russian Academy of Sciences, 2nd Brestskaya st., 19/18, 123056, Moscow, Russia

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 $Re \sim 10^{-1}$, 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.

Keywords: numerical modeling, elastic turbulence, hydrodynamic instability, Kolmogorov flow, numerical Godunov method.

UDC: 532.5

MSC: 76Fxx

Received November 1, 2024, published December 31, 2024

Language: English

DOI: 10.33048/semi.2024.21.B05