Mathematical Model of Three-Component Suspension Transport

Introduction. Prediction of suspension deposition zones is required to assess and minimize the negative impact on the ecosystem of the reservoir during dredging within the framework of large-scale engineering projects, prediction of suspension deposition zones is required to assess and minimize the negative impact on the ecosystem of the reservoir. It is necessary to build a mathematical model that takes into account many factors that have a significant impact on the accuracy of forecasts. The aim of the work is to construct a mathematical model of transport of multicomponent suspension, taking into account the composition of the soil (different diameter of the suspension particles), the flow velocity of the water flow, the complex geometry of the coastline and bottom, wind stresses and friction on the bottom, turbulent exchange, etc. Materials and Methods. A mathematical model for the transport of a multicomponent suspension and an approximation of the proposed continuous model with the second order of accuracy with respect to the steps of the spatial grid are described, considering the boundary conditions of the Neumann and Robin type. The approximation of the hydrodynamics model is obtained based on splitting schemes by physical processes, which guarantee fulfillment mass conservation for discrete model. Results. The proposed mathematical model formed the basis of the developed software package that allows to simulate the process of sedimentation of a multicomponent suspension. The results of the work of the software package on the model problem of sedimentation of a three-component suspension in the process of soil dumping during dredging are presented. Discussions and Conclusions. The mathematical model of transport of three-component suspension is described and software implemented. The developed software allows to simulate the process of deposition of suspended particles of various diameters on the bottom, and to evaluate its effect on the bottom topography and changes in the bottom composition. The developed software package also allows to analyze the process of sediment movement in the case of resuspension of multicomponent bottom sediments of the reservoir, which causes secondary pollution of the reservoi