Mathematical modeling of a turbulent fluid flow by using the quasihydrodynamic equations and k-omega turbulence model

In this paper, a mathematical model for solving the problem of developed turbulent flow in a channel is proposed. The equations describing the fluid flow are the Reynolds equations and the equations of the k-omega turbulence model reduced to a quasi-hydrodynamic form. For the numerical solution of the equations of the mathematical statement, a combined approach of the control volume method and the finite element method on triangular adaptive grids was used. To verify the proposed mathematical model, the problem of turbulent flow in a rectangular channel was solved. The results obtained showed a good agreement between the results of the proposed model and the results of direct numerical simulation in the turbulent sub-layer region. For further verification of the model, a number of problems of the turbulent flow past fixed sand dunes with different lee-slope angles were calculated. A comparative analysis of the calculated flow characteristics with experimental data was performed, which showed their qualitative and quantitative agreement, with the exception of the values of the turbulent kinetic energy in the case of flowing past low-angle dunes. Good agreement of the values of the Reynolds shear stress averaged over one dune and the total shear stress obtained using the proposed model with the experimental data allows us to use the proposed model to calculate the characteristics of a hydrodynamic flow passing over time-varying bed forms.