Geodesic
Application of a two-dimensional version of the linearized Godunov scheme to the numerical simulation of the Kolmogorov problem for a liquid polymer solution
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B64-B77 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. V. Denisenko; S. V. Fortova. Application of a two-dimensional version of the linearized Godunov scheme to the numerical simulation of the Kolmogorov problem for a liquid polymer solution. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B64-B77. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a73/

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