A comprehensive unsteady depth-averaged model with orthogonal curvilinear coordinate system

A mathematical model is developed here to solve unsteady depth-averaged shallow water flow equations. To enhance applicability, an orthogonal curvilinear coordinate system is used. The governing equations are solved by the two-step split-operator algorithm. Based on the finite-volume concept, all of the spatial derivatives are estimated with implicit central difference of second-order accuracy, while the convection terms are solved by a hybrid scheme. The effective stresses incorporates with a constant eddy-viscosity turbulence formulation to approximate the laminar and turbulent Reynolds stresses and with the secondary flow velocity profile proposed by de Vriend [1] to approximate the bend flow pattern. Two case studies including unsteady flow and bend flow are proposed herein to verify the model. Comparison with the experimental data shows that the model is efficient and robust. Finally, the model is applied to Tan-Shui River, a natural channel in Taiwan. The agreement between the computed results and field data is satisfactory.