Geodesic
Supercomputer simulation of hydrobiological processes of coastal systems
Matematičeskoe modelirovanie, Tome 34 (2022) no. 1, pp. 81-103.

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The paper discusses supercomputer modeling of the dynamics of plankton populations, including phyto- and zooplankton, in coastal systems. The mathematical model of the dynamics of planktonic populations includes a system of convection-diffusion-reaction equations with nonlinear members, allows to study the mechanism of external hormonal regulation based on the scenario approach. The proposed mathematical 3D model is linearized, its discretization is carried out, and on the basis of splitting by coordinates, a chain is obtained, consisting of two-dimensional and one-dimensional problems. For the numerical implementation of the proposed mathematical model of the hydrobiology of the coastal system in the form of a software module (SM), a multiprocessor computing system (MCS) was used, designed for massively parallel computations, its use made it possible to significantly reduce the operating time of the SM. To improve the accuracy of the calculations, a procedure was used to refine the solution on a sequence of thickening uniform rectangular grids. The influence of the mechanism of ectocrine regulation and the regime of nutrient intake on the production and destruction processes of plankton has been studied. The mathematical model includes a nonlinear dependence used to describe the growth rate of algal cells on the concentration of the metabolite, which made it possible to describe the ability of algal excretion products to control their growth even under conditions of massive influx of pollutants. The approach used meets modern concepts of the functioning of hydrobiocenosis. On the basis of the developed supercomputer-oriented software toolkit, not only direct trophic interactions, but also the actions of the waste products of individuals, which are mediated — chemical interactions, have been studied.
Keywords: mathematical model of hydrobiology, mechanism of external hormonal regulation, chemical interactions of plankton, splitting, algorithm, super-computer. 
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A. I. Sukhinov; A. V. Nikitina; A. M. Atayan; V. N. Litvinov; Yu. V. Belova; A. E. Chistyakov. Supercomputer simulation of hydrobiological processes of coastal systems. Matematičeskoe modelirovanie, Tome 34 (2022) no. 1, pp. 81-103. http://geodesic.mathdoc.fr/item/MM_2022_34_1_a5/

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