Analysis of the Friction Term in the One-Dimensional Shallow-Water Model

The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.