Eulerian-Lagrangian Linked Algorithm for Simulating Discontinuous Open Channel Flows

Standard finite difference and finite element methods result in poor and unsatisfactory solutions for near discontinuous open channel flows. The presence of oscillatory waves in the proximity of the discontinuous region is commonly addressed by adding external or internal dissipating mechanisms. A space-time finite element method based on the Galerkin formulation of the divergent form of the open channel flow equations is presented. The proposed Eulerian-Lagrangian linked algorithm demonstrates remarkable shock capturing properties while maintaining a high order of accuracy. No extraneous parameters are required to dissipate the parasitic oscillations. Results are presented for a number of flow conditions that lead to the formation of discontinuity and shocks. The improvement over other techniques is demonstrated by comparing the solution with finite element and finite difference methods.