A finite element approach to open channel flow
A dissipative Galerkin scheme has been developed for the study of the propagation of hydraulic jumps and bores in open channels. It uses the basis function to weight the temporal terms and an asymmetric weighting function to weight the convection terms. The scheme has been improved with routines that both apply the asymmetric weighting function only in the region of the shock and proportion the use of the asymmetric weighting function according to the magnitude of the local spurious oscillations. The introduced variability in the model improved the performance of the model in all examples tested. This scheme was compared to a Galerkin scheme with a symmetric weighting function instead of the basis function weighting the temporal terms and without the improved routines for applying the weighting functions. The scheme with the routines for proportionally applying the spatial weighting functions compared favorably.