vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2018-2-67-75vmait-70Research ArticleСтатьиРазработка модели транспорта и трансформации соединений азота, фосфора и кремния в мелководном водоемеDevelopment the transport and transportation model of nitrogen, phosphorus and silicon compounds in shallow watershttps://orcid.org/0000-0002-9878-0900СеменякинаАлёна АлександровнаSemenyakinaAlona Aleksandrovna

Семенякина Алёна Александровна, Научно-исследовательский центр супер-ЭВМ и нейрокомпьютеров (347900, Россия, Ростовская область, г. Таганрог, пер. Итальянский, дом 106), кандидат технических наук, научный сотрудник

Semenyakina Alona Aleksandrovna, Supercomputers and Neurocomputers Research Center, Co Ltd. (Italyansky lane, 106, Taganrog, Russian Federation), Candidate of Technical Science, Researcher

j.a.s.s.y@mail.ruhttps://orcid.org/0000-0002-5277-8485СумбаевВладимир ВалерьевичSumbaevVladimir Valeryevich

Сумбаев Владимир Валерьевич, Южный Федеральный Университет (347928, Россия, Ростовская область, г. Таганрог, пер. Некрасовский, 44), аспирант

Sumbaev Vladimir Valeryevich, Southern Federal University (Nekrasovsky lane, 44, Taganrog, Russian Federation), graduate student

valdec4813@mail.ruhttps://orcid.org/0000-0001-9656-8466ПроценкоСофья ВладимировнаProtsenkoSofya Vladimirovna

Проценко Софья Владимировна, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), аспирант

Protsenko Sofya Vladinirovna, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), postgraduate student

rab55555@rambler.ruНаучно-исследовательский центр супер-ЭВМ и нейрокомпьютеров (347900, Россия, Ростовская область, г. Таганрог, пер. Итальянский, дом 106)РоссияSupercomputers and Neurocomputers Research Center, Co Ltd. (Italyansky lane, 106, Taganrog, Russian Federation)Russian FederationЮжный Федеральный Университет (347928, Россия, Ростовская область, г. Таганрог, пер. Некрасовский, 44)РоссияSouthern Federal University (Nekrasovsky lane, 44, Taganrog, Russian Federation)Russian FederationДонской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian Federation2018280320232270Copyright © Семенякина А.А., Сумбаев В.В., Проценко С.В., 20232023Семенякина А.А., Сумбаев В.В., Проценко С.В.Semenyakina A.A., Sumbaev V.V., Protsenko S.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/70

В работе приведены стехиометрические соотношения питательных биогенных веществ вещество. Рассмотрены модели наблюдений, описывающие потребление, накопление фитопланктоном питательных веществ и скорость роста фитопланктона. Построена и исследована трехмерная математическая модель трансформации форм фосфора, азота и кремния в задаче динамики фитопланктона для мелководных водоемов, учитывающая конвективный и диффузионный переносы, поглощение и выделение питательных веществ фитопланктоном, циклы превращений форм фосфора, азота и кремния.

The paper covers stoichiometric ratios of nutrients for phytoplankton algae on the basis of which a limiting substance can be determined. Observational models describing the consumption, accumulation of nutrients by phytoplankton and the growth rate of phytoplankton are considered. Three-dimensional mathematical transformation model of phosphorus, nitrogen and silicon forms in the problem of phytoplankton dynamics for shallow waters is developed and researched. It takes into account the convective and diffusive transports; absorption and isolation of nutrients by phytoplankton; transformation cycles of phosphorus, nitrogen and silicon forms.

математическая модельтрансформациябиогенные веществафитопланктонстехиометрические соотношениябиогеохимический циклmathematical modeltransformationbiogenic substancesphytoplanktonstoichiometric ratiosbiogeochemical cycleРабота выполнена по теме № 2.6905.2017/БЧ в рамках выполнения госзадания Минобрнауки России в части НИР.The research is done on theme no. 6905.2017/БЧ within the frame of the government task of the Ministry of Education and Science of the Russian Federation in R&D.ReferencesVan Straten G., Keesman K.J. Uncertainty propagation and speculation in projectiveVan Straten G., Keesman K.J. Uncertainty propagation and speculation in projectiveforecasts of environmental change: a lake eutrophication example // Journal of Forecasting. – 1991.forecasts of environmental change: a lake eutrophication example // Journal of Forecasting. – 1991.– №10. – pp. 163-190.– №10. – pp. 163-190.Park R.A. A generalized model for simulating lake ecosystems // Simulation. – 1974. – №23 (2). – pp. 33-50.Park R.A. A generalized model for simulating lake ecosystems // Simulation. – 1974. – №23 (2). – pp. 33-50.Bierman V.J., Verhoff F.H., Poulson T.C., Tenney M.W. Multinutrient dynamic models of algal growth and species competition in eutrophic lakes // Modeling the eutrophication process. - Ann Arbor: Ann Arbor Science, 1974.Bierman V.J., Verhoff F.H., Poulson T.C., Tenney M.W. Multinutrient dynamic models of algal growth and species competition in eutrophic lakes // Modeling the eutrophication process. - Ann Arbor: Ann Arbor Science, 1974.Chen C.W. Concepts and utilities of ecologic models // Journal of Sanitary Engineering Division, ASCE. – 1970. – No.96 (5). – pp. 1085-1097.Chen C.W. Concepts and utilities of ecologic models // Journal of Sanitary Engineering Division, ASCE. – 1970. – No.96 (5). – pp. 1085-1097.Jorgensen S.E. An eutrophication model for a lake // Ecological Modelling. – 1976. – No.2(2). – Рp. 147-165.Jorgensen S.E. An eutrophication model for a lake // Ecological Modelling. – 1976. – No.2(2). – Рp. 147-165.Jorgensen S.E., Mejer H., Friis M. Examination of a lake model // Ecological Modelling. – 1978. – No.4 (2-3). – pp. 253-278.Jorgensen S.E., Mejer H., Friis M. Examination of a lake model // Ecological Modelling. – 1978. – No.4 (2-3). – pp. 253-278.Brodskii A. K. A short course on General ecology: a textbook for Universities. - St. Petersburg: Dean, 2000. – 224 p.Brodskii A. K. A short course on General ecology: a textbook for Universities. - St. Petersburg: Dean, 2000. – 224 p.Williams B.J. Hydrobiological modelling. - University of Newcastle, NSW, Australia: www.lulu.com, 2006. – 680 p.Williams B.J. Hydrobiological modelling. - University of Newcastle, NSW, Australia: www.lulu.com, 2006. – 680 p.Epply R.W., Rogers J.N., McCarthy J.J. Half-saturation constants for uptake of nitrate and ammonium by marine phytoplankton // limnology and Oceanography. – 1969. – No.14. – pp. 912-920.Epply R.W., Rogers J.N., McCarthy J.J. Half-saturation constants for uptake of nitrate and ammonium by marine phytoplankton // limnology and Oceanography. – 1969. – No.14. – pp. 912-920.Redfield A.C. The biological control of chemical factors in the environment // American Scientist. – 1958, №46. – pp. 205-222.Redfield A.C. The biological control of chemical factors in the environment // American Scientist. – 1958, №46. – pp. 205-222.Samarskii A.A., Vabischevich P. N. Numerical methods for solving convection-diffusion problems. – M.: Edditorial URSS, 1999.Samarskii A.A., Vabischevich P. N. Numerical methods for solving convection-diffusion problems. – M.: Edditorial URSS, 1999.Goloviznin V. M., Samara A. A. Difference approximation of convective transport with spatial splitting of time derivative // Mathematical Models and Computer Simulations. – 1998. – Vol. 10, No.1. – pp. 86-100.Goloviznin V. M., Samara A. A. Difference approximation of convective transport with spatial splitting of time derivative // Mathematical Models and Computer Simulations. – 1998. – Vol. 10, No.1. – pp. 86-100.Sukhinov A.I., Chistyakov A.E., Iakobovski M.V. Accuracy of the numerical solution of diffusion-convection equation based on difference schemes of second and fourth orders of approximation order // Vestn. SUSU. Ser. Calc. mod. inform. – 2016. – Vol. 5, No.1. – pp. 47-62.Sukhinov A.I., Chistyakov A.E., Iakobovski M.V. Accuracy of the numerical solution of diffusion-convection equation based on difference schemes of second and fourth orders of approximation order // Vestn. SUSU. Ser. Calc. mod. inform. – 2016. – Vol. 5, No.1. – pp. 47-62.Sukhinov A.I., Belov Yu.V. Mathematical model of transformation of the phosphorus, nitrogen and silicon forms in a moving turbulent water environment in problems of plankton populations dynamics // Engineering journal of Don. – 2015. – Vol. 37, No.3. – pp. 50.Sukhinov A.I., Belov Yu.V. Mathematical model of transformation of the phosphorus, nitrogen and silicon forms in a moving turbulent water environment in problems of plankton populations dynamics // Engineering journal of Don. – 2015. – Vol. 37, No.3. – pp. 50.Sukhinov A.I., Khachunts D.S., Chistyakov A.E. A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation // Computational Mathematics and Mathematical Physics. – 2015. – Vol. 55, No.7. – pp. 1216-1231.Sukhinov A.I., Khachunts D.S., Chistyakov A.E. A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation // Computational Mathematics and Mathematical Physics. – 2015. – Vol. 55, No.7. – pp. 1216-1231.Sukhinov A.I., Nikitina A.V., Chistyakov A.E. Modeling of biological rehabilitation scenario of the Azov Sea // Mathematical modeling. – 2012. – Vol. 24, No.9. – pp. 3-21.Sukhinov A.I., Nikitina A.V., Chistyakov A.E. Modeling of biological rehabilitation scenario of the Azov Sea // Mathematical modeling. – 2012. – Vol. 24, No.9. – pp. 3-21.Nikitina A.V., Sukhinov A.I., Ugolnitsky, G.A., Usov A.B., Chistyakov A.E., Puchkin M.V., Semenov I.S. Optimal management of sustainable development with biological rehabilitation of the Azov Sea // Mathematical modeling. – 2016. – Vol. 28, No.7. – pp. 96-106.Nikitina A.V., Sukhinov A.I., Ugolnitsky, G.A., Usov A.B., Chistyakov A.E., Puchkin M.V., Semenov I.S. Optimal management of sustainable development with biological rehabilitation of the Azov Sea // Mathematical modeling. – 2016. – Vol. 28, No.7. – pp. 96-106.Nikitina A.V., Puchkin M.V., Semenov I.S., Sukhinov A.I., Ugolnitsky G.A., Usov A.B., Chistyakov A.E. Differential-game model of zamora prevention in shallow waters // Managing large systems. – 2015. – Issue 55. – pp. 343-361.Nikitina A.V., Puchkin M.V., Semenov I.S., Sukhinov A.I., Ugolnitsky G.A., Usov A.B., Chistyakov A.E. Differential-game model of zamora prevention in shallow waters // Managing large systems. – 2015. – Issue 55. – pp. 343-361.Trân J.K. A predator-prey functional response incorporating indirect interference and depletion // Verh. Internat. Verein. Limnol. – 2008. – Vol. 30, Pt 2. – pp. 302-305.Trân J.K. A predator-prey functional response incorporating indirect interference and depletion // Verh. Internat. Verein. Limnol. – 2008. – Vol. 30, Pt 2. – pp. 302-305.Petrov Igor B. Application of grid-characteristic method for numerical solution of deformable solid mechanics dynamical problems // Computational Mathematics and Information Technologies. – 2017. Vol. 1, No 1. – pp. 1-20.Petrov Igor B. Application of grid-characteristic method for numerical solution of deformable solid mechanics dynamical problems // Computational Mathematics and Information Technologies. – 2017. Vol. 1, No 1. – pp. 1-20.Sukhinov A.I., Sidoryakina V.V., Sukhinov A.A. Sufficient convergence conditions for positive solutions of linearized two-dimensional sediment transport problem // Computational Mathematics and Information Technologies. – 2017. Vol. 1, No 1. – pp. 21-35.Sukhinov A.I., Sidoryakina V.V., Sukhinov A.A. Sufficient convergence conditions for positive solutions of linearized two-dimensional sediment transport problem // Computational Mathematics and Information Technologies. – 2017. Vol. 1, No 1. – pp. 21-35.Nikitina A.V., Semenyakina A.A. Mathematical modeling of eutrophication processes in Azov Sea on supercomputers // Computational Mathematics and Information Technologies. – 2017. Vol.1, No 1. – pp. 82-101.Nikitina A.V., Semenyakina A.A. Mathematical modeling of eutrophication processes in Azov Sea on supercomputers // Computational Mathematics and Information Technologies. – 2017. Vol.1, No 1. – pp. 82-101.Chistyakov A.E., Protsenko E.A., Timofeeva E.F. Mathematical modeling of oscillatory processes with a free boundary // Computational Mathematics and Information Technologies. – 2017. Vol.1, No 1. – pp. 102-112.Chistyakov A.E., Protsenko E.A., Timofeeva E.F. Mathematical modeling of oscillatory processes with a free boundary // Computational Mathematics and Information Technologies. – 2017. Vol.1, No 1. – pp. 102-112.Tyutyunov Yu., Senina I., Arditi R. Clustering due to acceleration in the response to population gradient: a simple self-organization model // The American Naturalist. – 2004, 164. – pp. 722-735.Tyutyunov Yu., Senina I., Arditi R. Clustering due to acceleration in the response to population gradient: a simple self-organization model // The American Naturalist. – 2004, 164. – pp. 722-735.Volterra V. Variations and fluctuations of the number of individuals in animal species living together // Rapp. P. – V. Reun. Cons. Int. Explor. Mer. – 1928. 3, pp. 3-51.Volterra V. Variations and fluctuations of the number of individuals in animal species living together // Rapp. P. – V. Reun. Cons. Int. Explor. Mer. – 1928. 3, pp. 3-51.Yakushev E.V., Mikhailovsky G.E. Mathematical modeling of the influence of marine biota on the carbon dioxide ocean-atmosphere exchange in high latitudes // Air-Water Gas Transfer, Sel. Papers, Third Int. Symp., Heidelberg University, ed. by B. Jaehne and E.C. Monahan, AEON Verlag & Studio, Hanau. – 1995. – pp. 37-48.Yakushev E.V., Mikhailovsky G.E. Mathematical modeling of the influence of marine biota on the carbon dioxide ocean-atmosphere exchange in high latitudes // Air-Water Gas Transfer, Sel. Papers, Third Int. Symp., Heidelberg University, ed. by B. Jaehne and E.C. Monahan, AEON Verlag & Studio, Hanau. – 1995. – pp. 37-48.

The authors declare that there are no conflicts of interest present.