Abstract
Introduction.The solution to the problem of transformation of phosphorus, nitrogen and silicon forms is studied. This problem arises under modeling phytoplankton dynamics in shallow-water bodies including the Azov Sea. The phytoplankton dynamics model is formulated as a boundary value problem for the system of diffusion-convection-response equations and takes into account the absorption and release of nutrients by phytoplankton, as well as the transition of nutrients from one compound to another. To calculate the initial conditions and parameters of the equations under which the steady-state regime occurs, the software is developed, which is based on the model describing changes in phytoplankton concentrations without considering current effects. This model is represented by a system of inhomogeneous differential equations. Based on the developed software, the initial conditions and parameters of the phytoplankton dynamics model in the Azov Sea are calculated experimentally.Materials and Methods.A 3D model of phytoplankton dynamics is considered taking into account the transformation of phosphorus, nitrogen and silicon compounds based on the system of nutrient transport equations. The case of a spatially uniform distribution of substances is considered to specify the parameters of the model at which the stationary modes occur. Because of simplification, a system of ordinary differential equations solved through the Runge-Kutta method is obtained.Research Results. The software is developed to specify the initial conditions and parameters of the phytoplankton dynamics model considering the transformation of phosphorus, nitrogen and silicon compounds. Several numerical experiments are performed under the assumption that the development of phytoplankton is limited by a single biogenic substance. As a result of the computational experiment, it can be seen that with the obtained values of the initial concentrations and parameters of the equations, stationary modes occur for the system of ordinary differential equations describing the case of the spatially uniform distribution of substances.Discussion and Conclusions.The mathematical model of the transformation of phosphorus, nitrogen and silicon forms in the problem of phytoplankton dynamics is studied. Stationary modes for the system of ordinary differential equations are obtained, for which the values of the system parameters and initial conditions are determined. The results obtained can be used in further simulation of the phytoplankton dynamics considering the transformation of phosphorus, nitrogen and silicon compounds with account for convection-diffusion, salinity, and temperature.
Highlights
The solution to the problem of transformation of phosphorus, nitrogen and silicon forms is studied. This problem arises under modeling phytoplankton dynamics in shallow-water bodies including the Azov Sea
The phytoplankton dynamics model is formulated as a boundary value problem for the system of diffusion-convection-response equations and takes into account the absorption and release of nutrients by phytoplankton, as well as the transition of nutrients from one compound to another
A 3D model of phytoplankton dynamics is considered taking into account the transformation of phosphorus, nitrogen and silicon compounds based on the system of nutrient transport equations
Summary
Исследование стационарных решений задачи динамики фитопланктона с учетом трансформации соединений фосфора, азота и кремния *. Работа посвящена исследованию решения задачи трансформации форм фосфора, азота и кремния. Данная проблема возникает при моделировании динамики фитопланктона в мелководных водоемах, в том числе в Азовском море. Для расчета начальных условий и параметров уравнений, при которых наступает стационарный режим, разработано программное обеспечение, основой которого послужила модель, описывающая изменения концентраций фитопланктона без учета влияния течений. Данная модель представлена системой неоднородных обыкновенных дифференциальных уравнений. Рассматривается трехмерная модель динамики фитопланктона с учетом трансформации соединений фосфора, азота и кремния, основанная на системе уравнений транспорта биогенных веществ. При которых наступают стационарные режимы, рассматривается случай пространственно-однородного распределения субстанций. Разработано программное обеспечение для уточнения начальных условий и параметров модели динамики фитопланктона с учетом трансформации соединений фосфора, азота и кремния.
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