Numerical simulation of transcritical flow in open channels

The term transcritical flow denotes the existence of both subcritical and supercritical flow regimes in an open-channel system. It is similar to transonic flow in gas dynamics. Transcritical flow is encountered in many engineering problems of practical interest; irrigation networks, for example, often involve transcritical flow caused by the dynamic operation of hydraulic structures. This paper presents a two-step, predictor-corrector, implicit numerical scheme for simulating transcritical flows of practical interest. The proposed scheme is second-order accurate in time and space and requires inversion of only bidiagonal matrices. It is, therefore, computationally efficient and can readily accommodate hydraulic structures. To suppress spurious oscillations near regions of steep gradients and facilitate the resolution of hydraulic jumps, nonlinear (adaptive) second-difference artificial dissipation terms are added explicitly. The scheme is validated by calculating a series of applications of practical interest. The computed solutions are compared with previously published results and exact solutions where available. It is shown that the proposed scheme is robust and accurate, has reasonable shock-capturing capabilities, and can easily simulate hydraulic structures.