Geodesic
Mathematical modeling of biogeochemical cycles in coastal systems of the South of Russia
Matematičeskoe modelirovanie, Tome 33 (2021) no. 3, pp. 20-38.

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This work is devoted to the development and study of a mathematical model of biogeochemical processes occurring in the coastal systems of southern Russia, which makes it possible to improve the accuracy of predicting the dynamics of phytoplankton populations, taking into account the effect of salinity and temperature on their development and transformation of forms of phosphorus, nitrogen and silicon. The study of the continuous model is carried out, the linearization of nonlinear functions of sources is carried out, and sufficient conditions for the uniqueness of solutions of chains of initial-boundary value problems interrelated in initial and final conditions are obtained, and a theorem is formulated. Difference schemes are constructed based on improved discretization of advective terms of linearized initial-boundary value problems on a spatial grid, based on linear combinations of cabaret and central-difference schemes. These schemes have better accuracy and increased stability margin (applicable in a wider range of grid Peclet numbers) compared to traditional difference schemes. Initial conditions and refined parameters of the system of equations are obtained, salinity and temperature fields for the Azov Sea, which have a sufficient degree of smoothness, are reconstructed from hydrographic maps. A software package was developed and a numerical experiment was carried out on diagnostic and predictive modeling of biogeochemical processes in the Azov Sea in the summer under conditions of modern salinity. The simulation results are consistent with the available observational data.
Keywords: mathematical model, biogeochemical cycles, linearization, difference scheme, software package, salinization. 
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A. I. Sukhinov; Y. V. Belova; A. E. Chistyakov. Mathematical modeling of biogeochemical cycles in coastal systems of the South of Russia. Matematičeskoe modelirovanie, Tome 33 (2021) no. 3, pp. 20-38. http://geodesic.mathdoc.fr/item/MM_2021_33_3_a1/

[1] P. A. Balykin, D. N. Kutsyn, A. M. Orlov, “Izmeneniia solenosti i vidovogo sostava ikhtiophauny v Azovskom more”, Okeanologiia, 59:3 (2019), 396–404

[2] G. G. Matishov, Iu. M. Gargopa, S. V. Berdnikov, S. L. Dzheniuk, Zakonomernosti ekosistemnykh protsessov v Azovskom more, Nauka, M., 2006, 304 pp.

[3] Iu. A. Dombrovskii, V. G. Ilichev, V. V. Seliutin, F. A. Surkov, Teoreticheskie i prikladnye aspekty modelirovaniia pervichnoi produktivnosti vodoemov, Izd-vo Rostovskogo universiteta, Rostov n/D, 1990, 176 pp.

[4] N. D. Lewis, M. N. Breckels, M. Steinke, E. A. Codling, A. Morozov, Y. V. Tyutyunov, “Multitrophic interactions in the sea: assessing the effect of infochemical-mediated foraging in a 1-D spatial model”, Mathematical Modelling of Natural Phenomena, 8:6 (2013), 25–44 | DOI | MR | Zbl

[5] V. Yu. Glotov, V. M. Goloviznin, S. A. Karabasov, A. P. Markeshteijn, “New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations”, Comp. Math. Math. Phys., 54:2 (2014), 315–334 | DOI | MR | Zbl

[6] A. I. Sukhinov, A. E. Chistiakov, E. A. Protsenko, “O raznostnykh skhemakh kabare i krest”, Vych. met. programmirovanie, 20:2 (2019), 170–181

[7] A. I. Sukhinov, A. E. Chistyakov, A. V. Shishenya, “Error estimate for diffusion equations solved by schemes with weights”, MM CS, 6:3 (2014), 324–331 | MR | Zbl

[8] A. I. Sukhinov, Iu. V. Belova, “Matematicheskaia model transformatsii form fosfora, azota i kremniia v dvizhushcheisia turbulentnoi vodnoi srede v zadachakh dinamiki planktonnykh populiatsii”, Inzhenernyi vestnik Dona, 2015, no. 3 (37), 50

[9] A. I. Sukhinov, A. E. Chistyakov, E. V. Alekseenko, “Numerical realization of the three-dimensional model of hydrodynamics for shallow water basins on a high-perfor-mance system”, Mathematical Models and Computer Simulations, 3:5 (2011), 562–574 | DOI | MR | Zbl

[10] A. I. Sukhinov, Iu. V. Belova, A. E. Chistiakov, “Reshenie zadachi perenosa veshchestv pri bolshikh chislakh Pekle”, Vuch. met. programmirovanie, 18:4 (2017), 371–380

[11] A. I. Sukhinov, A. E. Chistiakov, M. V. Iakobovskii, “Tochnost chislennogo resheniia uravneniia diffuzii-konvektsii na osnove raznostnykh ckhem vtorogo i chetvertogo poriadkov pogreshnosti approksimatsii”, Vestnik IuUrGU. Ser. Vych. matem. Inform., 5:1 (2016), 47–62

[12] A. I. Sukhinov, A. E. Chistyakov, Y. V. Belova, “The difference scheme for the two-dimensional convection-diffusion problem for large Peclet numbers”, MATEC Web of Conferences, 226:04030 (2018)

[13] Iu. V. Belova, A. M. Ataian, A. E. Chistiakov, A. V. Strazhko, “Issledovanie statsionarnykh reshenii zadachi dinamiki fitoplanktona s uchetom transformatsii soedinenii fosfora, azota i kremniia”, Vestnik Donskogo gosudarst. tekhnicheskogo univers, 19:1 (2019), 4–12

[14] A. I. Sukhinov, A. E. Chistyakov, “Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator”, Mathematical Models and Computer Simulations, 4:4 (2012), 398–409 | DOI | MR | Zbl

[15] A. E. Chistiakov, A. A. Semeniakina, “Primenenie metodov interpoliatsii dlia vosstanovleniia donnoi poverkhnosti”, Izvestiia IuFU. Tekhnicheskie nauki, 2013, no. 4 (141), 21–28

[16] A. I. Sukhinov, A. V. Shishenya, “Enhancement of SSOR method efficiency on the base of improved spectral estimations”, Math. Mod. Comp. Simul., 5:3 (2013), 257–265 | DOI | MR | Zbl

[17] A. I. Sukhinov, A. E. Chistiakov, “Parallelnaia realizatsiia trekhmernoi modeli gidrodinamiki melkovodnykh vodoemov na supervychislitelnoi sisteme”, Vychislitelnye metody i programmirovanie, 13:1 (2012), 290–297

[18] Visible Earth. A catalog of NASA images and animations of our home planet, (data obrascheniya: 28.10.2019) https://visibleearth.nasa.gov/images/71786/phytoplankton-bloom-in-the-sea-of-azov