The purpose of the article is to develop the required and sufficient conditions under which numerical methods can be used for engineering calculations and for scientific research of hydrodynamic processes in solving practical problems related to predicting the spread of pollutants in water bodies and streams. The conducted studies consisted in comparing the results of laboratory experiments and mathematical modelling, in particular the distribution of heat in a stream with different temperature in water layers was studied. To check the adequacy of the proposed numerical models, calculations were performed and comparisons were made with the results of experimental data. The obtained results allowed to determine the boundaries of the qualitative difference in the flow behaviour for different numbers of Froude and Reynolds. The accuracy of the method was also studied. A number of additional requirements for numerical models were proposed in addition to approcsimation and stability, such as requirements of conservativeness (divergence), existence of trivial solutions on grids, possibility to calculate highly unsteady, quasi-stable, pulsating and stationary flows, requirement of invariance of linearized equations, as well as the requirement of a one-dimensional scheme to be a consequence of a two-dimensional scheme. Distribution of velocities of wind currents using a three-dimensional and two-dimensional model was studied for a real object. A shallow-water bay of the Aral Sea was chosen as the object for the research. Comparison of the calculation results for both models showed that the flow velocity fields, as well as the distribution of pollutants in shallow waters, can be performed using a two-dimensional model.
An experimental and theoretical investigation of particle–wall impacts in a T-junction
