Fast Computational Models in Water Use Problems - Mashykhina, P. B.; Biliaiev, M. M.; Kalashnykov, A. V.; Tsurkan, V. V.; Nabiiev, Zaur; Sieriedin, B. V. (Science and Transport Progress, 2025)
Purpose. At the stage of preliminary design of various structures in water supply and wastewater systems, it is necessary to have a set of mathematical models to perform serial calculations to assess the efficiency of these structures in different conditions. Mathematical models are needed that take into account the basic physical factors. Such models are mathematical models of hydrodynamics and mass transfer. The complexity of the mathematical formulation of mass transfer problems for water supply and wastewater treatment systems lies in the use of numerical methods. This is due to the fact that multifactor differential equations are used in fundamental models of continuum mechanics. For practical use, it is especially important to have fast numerical models to perform serial calculations during a working day. The main purpose of this work is to develop fast-calculating numerical models for solving a set of problems in the field of water supply and sewerage. Methodology. The fundamental equations of continuum mechanics are used to solve mass transfer problems: the equation for the velocity potential, the filtration equation, and the equation for convective-diffusive impurity transfer. Finite difference schemes are used for numerical integration of the modeling equations. The construction of finite-difference schemes is carried out in such a way as to obtain equations for which explicit formulas can be used to solve. The numerical integration of the modeling equations is carried out on a rectangular difference grid. Findings. A set of numerical models has been developed that can be used at the stage of preliminary design of water supply and wastewater treatment facilities. The constructed numerical models take into account the main physical factors that affect the processes of mass transfer in these structures. Originality. A set of mathematical models is proposed to study multifactorial mass transfer processes in water supply and sewage facilities. Numerical models take into account the convective diffusion process of impurity propagation. Practical value. The constructed numerical models can be used in the design of pressure filters, water intakes, and wastewater neutralization facilities.