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The paper is devoted to mathematical modelling and numerical computations of a nonstationary free boundary problem. The model is based on processes of molecular diffusion of some products of chemical decomposition of a solid organic substance concentrated in bottom sediments. It takes into account non-stationary multi-component and multi-stage chemical decomposition of organic substances and the processes of sorption desorption under aerobic and anaerobic conditions. Such a model allows one to obtain quantitative estimates of incoming solute organic substances of anthropogenic origin having different molecular weights from the bottom sediments into water and to study the influence of seasonal variations of the concentration of solute oxygen in the near-bottom water on the direction of exchange processes in the system “waterbottom”. Identification of parameters of the mathematical model with the use of experimental data and with the employment of a priori information of the model's structure is carried out. Comparison of the numerical simulations with experimental data is conducted to the end of verification of efficiency and plausibility of the proposed mathematical model of secondary pollution. It implies assessment of water quality on account of the processes of exchange in the system “waterbottom”. The results of computations of non-stationary fluxes at the boundary “waterbottom” are analyzed. A model example is used to estimate the potentials of the biogenic load on the water reservoir.

mathematical modelling of natural phenomena

Modeling Non-Stationary Processes of Diffusion of Solute Substances in the Near-Bottom Layer ofWater Reservoirs: Variation of the Direction of Flows and Assessment of Admissible Biogenic Load