Advances in calculation methods for super-critical flow in spillway channels

A calculation method is presented for applications to steady supercritical and transcritical flow in spillway channels. The method solves the two-dimensional nonlinear shallow water equations using a cell-centered finite-volume approach. High spatial resolution of shock waves and other steep flow features is achieved by employing MUSCL reconstruction and an approximate Riemann solver for the flux evaluations at each cell interface. The method can be implemented on boundary-conforming meshes to more accurately map the wide range of geometries that may occur in practice. Six analytical test problems are proposed for the validation of calculation methods applied to steady supercritical flow. These problems are used to validate the proposed flow solver, which is then applied to the case of steady supercritical flow in curved channel transition, and comparisons are made with published data. Despite limitations in the shallow water model, the results show satisfactory agreement with data for the maximum rise in water level through the standing oblique shock waves.