Quasi-three-dimensional numerical model for flow through flexible, rigid, submerged and non-submerged vegetation

The effects of the resistance caused by vegetation on flow velocity and water depth has become a major interest for ecologists and those who deal with river restoration projects. Some numerical and experimental works have been performed to analyse and formulate the drag effects induced by vegetation. Here we introduce a quasi-three-dimensional (Q3D) numerical solution, which is constructed by coupling the finite volume solution of the two-dimensional shallow water equations with a finite difference solution of Navier–Stokes equations for vertical velocity distribution. The drag forces are included in both sets of equations. Turbulence shear stresses are computed in two alternative ways: the parabolic eddy viscosity approach with a correction term introduced in this study, and a combination of the eddy viscosity and mixing length theories in the vertical direction. In order to deal with flexible vegetation, a cantilever beam theory is used to compute the deflection of the vegetation. The model COMSIM (complex flow simulations) has been developed and applied in experimental cases. The results are shown to be satisfactory.