Discontinuous Galerkin method for 1D river flows

Draoui, Insaf [UCL] Lambrechts, Jonathan [UCL] Legat, Vincent [UCL] Soares Frazao, Sandra [UCL] Hoitink, Ton (A.J.F.) [Wageningen University] Deleersnijder, Eric [UCL]

We study the stability of various formulations of the momentum conservation equation for 1D flows in real rivers. The 1D Saint-Venant equations are solved using a Discontinuous Galerkin numerical method and applied to relevant test cases. We explain how to deal with arbitrary cross sections. The water level and water depth as direct terms in the equations hamper the appropriate treatment of arbitrary cross sectional areas. Applying Newton s second law of motion to a control volume leads to a more stable formulation. The modelling of connections of several channels is also addressed with a formulation based on curvilinear coordinates. The 1D model in this case is validated based on a comparison with a 2D model for the different configurations.