Mathematical modeling of eutrophication processes in Azov Sea on supercomputers

Abstract

Introduction. The paper is devoted to the research of effective numerical methods for solving eutrophication problem of shallow waters taking into account water environment, spatiallynonuniform distribution of temperature and salinity, microturbulent diffusion, gravitational sedimentation, and spreading of biogenic pollution, oxygen, phyto-and zooplankton, etc. The simulation objects are shallow waters -the Azov Sea and Taganrog Bay. Materials and Methods. The mathematical model of eutrophication of shallow waters was developed. Parallel implementation was performed for computationally laborious convection-diffusion problems, taking into account the architecture and parameters of supercomputers based on the decomposition methods of grid domains. We determined that the maximum acceleration was 43 times on 128 computational nodes. We developed two algorithms including the algorithm based on the kmeans method for data distribution between processors in parallel implementation. Due to the using these algorithms, the efficiency of algorithm for solving the problem is increased on 15% compared to the algorithm of the standard partition of computational domain. Results. New mathematical models and software complex were developed for mathematical modeling of eutrophication processes in shallow waters. The concentrations of pollutants and plankton calculated for different wind situations were taken into consideration, if the relative error did not exceed 30%. Due to expedition researches the primary verification of the model of ecosystem of the Azov Sea was performed. The problem of modeling and forecasting the state of water ecosystems of the Azov Sea in conditions of anthropogenic influence and comprehensive research of the unique water object was implemented. Because of the water object is shallow, it's more affected by anthropogenic influence. The software complex, combining mathematical models and databases, was designed. Using this complex we researched conditions which are contributed by the eutrophication processes in shallow waters. Discussion and Conclusions. Due to the solving the water ecology problem we can forecast different scenario of changing the water quality in shallow waters, and to investigate the mechanisms of formation of zones with low oxygen content.

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