Computation of free surface flows. Part III. Steady supercritical flow using a generalized lagrangian method

Abstract

A second order Godunov-type nonoscillatory scheme is presented for solving the steady shallow water equations in generalized Lagrangian formulation and applied to compute steady supercritical flows. The Lagrangian distance and a stream function are used as the independent variables which have intrinsic flow adaptive property embedded. Numerical examples involving oblique hydraulic jumps, tangential discontinuities and negative waves and their interactions are given. It is illustrated that all the flow discontinuities in steady supercritical flows can be accurately and efficiently computed by using the generalized Lagrangian method in junction with the present high resolution scheme.