Mathematical model of shallow water self-purification process

The paper covers the model of shallow water self-purification processes. The proposed mathematical model of biological kinetics is based on a system of non-stationary convection-diffusion-reaction equations with nonlinear terms, taking into account the water flow movement, gravitational sedimentation of impurities, microturbulent diffusion, and the detritus decomposition as a result of activity the aerobic and anaerobic bacteria. Discretization is performed on the basis of a linear combination of central and Upwind Leapfrog difference schemes, which makes it possible to increase the solution accuracy of biological kinetics problem at large values of the grid Péclet number (Peh > 2). To solve high-dimensional SLAEs, a modified alternating-triangular method was used.