SPH modelling of turbulent open channel flow over and within natural gravel beds with rough interfacial boundaries

Smoothed Particle Hydrodynamics (SPH) is brought to a level that can be applied to simulate turbulent open channel flows over and within natural porous gravel beds. For this, improvements have been made with regards to i) turbulence modelling, ii) open boundaries (inflow and outflow), and iii) treatment of the rough interface boundary between the porous bed and the overlying free-flow. Flow through the porous bed is simulated macroscopically, and the coefficients of the drag closure model are carefully determined at different layers of the flow; the effect of turbulence is taken into account using a three-layer mixing-length model; and a porous inflow boundary at the inlet as well as an imaginary pressure wall at the outlet are introduced to obtain the required steady and uniform flow conditions. The developed model is then used to simulate eight test cases with two bed conditions, each with four flow conditions. Through the velocity analysis, a nearly S-shaped distribution is observed within the roughness layer for the present test cases. The comparison of the results of the velocity and shear stress with a set of experimental data reveals that the SPH model with the present drag and turbulence closure models as well as the proposed inflow/outflow boundary techniques is capable of simulating complex turbulent channel flows over highly sheared natural porous beds.