The current three-dimensional mathematical model of flow developed by the original ideal of Reynolds (1895) is based on the classical averaging method. This model is received  by the classical averaging method of velocity and pressure parameters from the three-dimensional Navier-Stokes equations system. These averaging parameters obtained by this classical approach are not generalized in comparison to ones  by the dual approach. This paper proposes a dual approach to  averaging of velocity and pressure  parameters of the three-dimensional Navier-Stokes equations. The model setup is more complicated than the classical model, the procedure can be repeated several times. In this paper, the authors perform twice: (i) for the first time: integrating the velocity and pressure parameters from time  t  to T_m, with time T_m<t+T, where T is the repeated period of parameters; (ii) for the second time: integral from time  t  to  t+T. Fluctuation quantities such as velocity and pressure in turbulent flow,  over time, are simulated using trigonometric Fourier series.

The three-dimensional flow model obtained from this dual approach could provide more accurate results than those given by the classical method proposed by Reynolds in 1895.