摘要：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 surveying of pollutants diffusion in water flows. The conducted studies consisted in the finding out conditions under which mathematical modelling using hydrodynamic equations allows to solve engineering problems of channel hydrodynamics and, in particular, to numerically simulate the transport of suspended particles in channels. A number of additional nature of numerical models were studied in addition to approximation and stability, such as averaging over probability and over time averaging. It was noted that only stationary processes could be described by equations if they are obtained from the Reynolds equations, i.e. when using the Reynolds equations, an important class of problems with a pulsating flow under constant boundary conditions is excluded from consideration. And, if the equations are obtained directly from the conservation laws, then all the desired variables have the meaning of actual quantities averaged over the scale. That is even in the case of statistically stationary flows, using such equations, it is possible to solve nonstationary problems on large time scales.
其他摘要：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 surveying of pollutants diffusion in water flows. The conducted studies consisted in the finding out conditions under which mathematical modelling using hydrodynamic equations allows to solve engineering problems of channel hydrodynamics and, in particular, to numerically simulate the transport of suspended particles in channels. A number of additional nature of numerical models were studied in addition to approximation and stability, such as averaging over probability and over time averaging. It was noted that only stationary processes could be described by equations if they are obtained from the Reynolds equations, i.e. when using the Reynolds equations, an important class of problems with a pulsating flow under constant boundary conditions is excluded from consideration. And, if the equations are obtained directly from the conservation laws, then all the desired variables have the meaning of actual quantities averaged over the scale. That is even in the case of statistically stationary flows, using such equations, it is possible to solve nonstationary problems on large time scales.
