Verification of 1-D transcritical flow model in channels

This paper deals with the use of high-resolution non-oscillatory shock-capturing difference schemes to solve steady and unsteady one-dimensional flows with steep waves in channels. Such transcritical flow may be either free surface (subcritical/supercritical) or free surface/pressurized in a pipe. The main features of a class of high-resolution schemes are described with reference to the unsteady one-dimensional shallow water equations. The operator splitting method is utilized to compute the flows with bottom slope and friction terms, and the method of characteristics with second-order accuracy is also incorporated in the present model to treat the external and internal boundary conditions. Numerical results are obtained for a series of one-dimensional test cases by means of the proposed model and are compared with analytical solutions or experimental measurements. It is shown that the proposed model is accurate, robust and highly stable in capturing strong gradients and discontinuities in such transcritical flows, and is a reliable mathematical model for one-dimensional practical hydraulic engineering applications.