Computational aspects of mathematical modeling of the shallow water hydrobiological processes

Paper covers the research of nonlinear effects in population dynamics of the pelengas commercial fish of the Azov Sea taking into account the Allee effect, competition for resources, taxis, catching, spatial distribution of biogenic matter and detritus based on a multi-species model of plankton and fish interaction. Discrete analogue of developed model problem of water ecology, included in a software complex, were calculated using schemes of second order of accuracy taking into account the partial filling of computational cells. The system of grid equations of large dimension, arising at discretization, has been solved on the basis of adaptive modified alternately triangual variational method. Effective parallel algorithms were developed for numerical implementation of biological kinetics problem and oriented on multiprocessor computer system and NVIDIA Tesla K80 graphics accelerator with the data storage format modification. Due to it, the reproduction processes of biogeocenose populations have been analyzed in real and accelerated time.