Numerical simulation of tidal bores and hydraulic jumps

An implicit finite difference formulation of the nonlinear shallow water equations is developed to allow for the treatment of tidal bores and hydraulic jumps. Five different schemes are investigated involving upwind treatment of convective terms, central differences combined with dissipative interface, forward time-centering and various combinations of these techniques. The schemes are analyzed with respect to their effective amplification portraits, and they are tested on periodic bores, uniform bores and steady hydraulic jumps. In this connection the model results are verified against analytical solutions and a numerical solution obtained with a Godunov Riemann solver. Scheme 4, which combines forward time centering and dissipative interface, is found to be superior to the others and it is applicable for Courant numbers within the range 0.25 to 1.5. This scheme is applied to a case study of the tidal bore in Huangzhou Bay and Qiantang River. The model results are shown to be in very good agreement with field data.