Mathematical Modelling

Mathematical models and methods of forecasting biological kinetics processes considering the oxygen regime

A. I. Sukhinov^a, Yu. V. Belova^a, I. Yu. Kuznetsova^ab, A. M. Atayan^a, A. E. Chistyakov<sup>a

a</sup> Don State Technical University, Rostov-on-Don, Russian Federation
^b Southern Federal University, Rostov-on-Don, Russian Federation

Abstract: This article describes a set of mathematical models that allow building medium-term forecasts of biological kinetics processes occurring in the presence of oxygen in an aquatic environment. The hydrodynamic model uses a regularizer according to B.N. Chetverushkin, which allows obtaining a wave equation for calculating pressure. The stability and approximation error of the difference scheme for the pressure calculation equation are studied. The use of this method made it possible to reduce the computational complexity of the pressure calculation problem. A software package based on integrated models of hydrodynamics and hydrobiology is built using MPI parallel programming technology. Distributions of concentrations of the main biogenic substances and phytoplankton populations are obtained depending on meteorological conditions. The parallel algorithms used in the study allow building medium-term forecasts of biogeochemical processes in coastal systems once in the accelerated time mode.

Keywords: model of biological kinetics, regularizer according to B.N. Chetverushkin, oxygen regime, parallel algorithms, Message Passing Interface.

UDC: 519.6

MSC: 92B05

Received: 28.01.2025

DOI: 10.14529/mmp250205