Simulation of flow in compound open-channel using a discontinuous Galerkin finite-element method with Smagorinsky turbulence closure

The small-scale spatial variability of eddy viscosity which is characteristic for the turbulent shear stress in compound open-channel flows was studied and investigated in this paper. Different options including a constant value, zero-equation, one-equation, two-equation, and Smagorinsky turbulence models for parameterizing the eddy viscosity were developed in the framework of the discontinuous Galerkin finite-element SLIM model and applied for presenting the complex velocity profile in two different experimental data sets of laboratory flumes. A very good qualitative agreement was achieved between numerical results and measurement data for both velocity and flow depth of all experimental data sets in general. In addition, the calculation results showed that the turbulent Smagorinsky empiricism allowed a better presentation of non-uniform velocity in the floodplain and transition regions between plain and main channels than the others in all calculated cases. This empiricism predicted a very close variation of eddy viscosity in comparison with the results calculated by the depth-averaged Reynolds' stress and the lateral gradient of longitudinal velocity. The eddy viscosity varies significantly in the channel section; in particular the small values often occurred around the middle location of floodplains and the central location of the main channel while the large values appeared in the transition regions, presenting different minimum and maximum values of eddy viscosity in each flow region. The effects of eddy viscosity variation on lateral distribution of velocity profile were also investigated and discussed.