Mathematical and Numerical Models of Hydrodynamics

Source abstract

Purpose. Mathematical modeling methods are widely used in the design of various water management structures (water intakes, horizontal or vertical sedimentation tanks, wastewater neutralization systems, filter-based water treatment systems, substance mixing systems, etc.). This is because conducting experimental research in this field requires significant time and expensive equipment. During design work, empirical models are typically used, which allow for the rapid determination of parameters for “standard” structures. However, for water management system structures with complex geometric shapes, such models are ineffective because they do not account for hydrodynamics. Therefore, a pressing task is the development of multifactorial numerical models to determine hydrodynamic regimes in water management system structures. The aim of this work is to develop numerical models based on finite-difference schemes. Methodology. Finite-difference schemes are used for the mathematical modeling of hydrodynamics in water-use structures. These schemes are used to numerically integrate the velocity potential equation, the Euler equations, and the Navier-Stokes equations. Findings. The numerical models discussed have been implemented in software. FORTRAN was used for programming. The computer programs developed are based on a modular design, which ensures a certain degree of «flexibility» when conducting computational experiments. Originality. A set of numerical models has been developed to solve hydrodynamic problems in water-use structures. The models were constructed using finite-difference methods for the numerical integration of the fundamental equations of continuum mechanics. Practical value. The numerical models developed may be useful in the design of new water management systems or the redesign of existing ones.