Advances in calculation methods for supercritical flow in spillway channels

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