The qualitative regularities of the eutrophication process of a shallow water research based on a biological kinetics mathematical model

Yu. V. Belova   ; E. O. Rahimbaeva   ; V. N. Litvinov   ; A. E. Chistyakov   ; A. V. Nikitina   ; A. M. Atayan

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 14-27

Résumé

The article is devoted to modeling the processes of eutrophication of a shallow water body on a computer system with distributed memory. The proposed mathematical model of biological kinetics is based on a system of non-stationary convection-diffusion-reaction equations with non-linear terms, takes into account the movement of water flow, gravitational settling of impurities, microturbulent diffusion, decomposition of detritus as a result of the activity of aerobic and anaerobic bacteria. The introduction of a non-linear dependence of the growth rate of phytoplankton and bacteria allows to describe the production-destruction processes in a reservoir, to control their dynamics under conditions of excessive intake of biogenic substances (nitrogen, phosphorus and silicon compounds), sulfur compounds, including hydrogen sulfide and sulfates, under various oxygen distribution modes, detritus, spatial and temporal variability of illumination, salinity and temperature, which corresponds to modern ideas about the functioning of the hydrobiocenosis of a shallow water body. The linearization of the continuous problem is carried out, its discrete analogue is constructed from the linearized model based on the splitting of the original three-dimensional problem into two-dimensional and one-dimensional. To build a discrete two-dimensional model, a linear combination of Upwind and Standard Leapfrog difference schemes was used, considering the partial filling of the calculation cells, which allowed to increase the accuracy of modeling the studied processes and phenomena. The results of diagnostic modeling of the processes of hydrogen sulfide contamination and self-purification of a shallow reservoir are presented.

Détail

Keywords: Azov Sea, eutrophication, mathematical modelling, explicit-implicit difference scheme, approximation error, distributed memory computing system.
Mots-clés : computational domain decomposition

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