Abstract
In this paper, we present a one step downstream characteristic Lagrangian hybrid method (DSCLH) for solution of the time-dependent open channel flow equations. It is a fixed-grid hybrid method, in which a numerically stable Lagrangian method is used to compute the nonlinear or linear convection process by convecting the grid downstream one step along the trajectory of a fluid particle. It significantly reduces numerical smoothing and simplifies Lagrangian advection since there is no need to determine the upstream interpolation points. It works well for both steady and unsteady state calculations where discontinuities are present. Solutions are found for the open channel flow equations using different initial and boundary conditions. Comparison with known results shows that the DSCLH method is both convergent and L ∞ stable. It can be applied to a wide range of shock problems and run for long times without oscillation. Certain fundamental conditions which are necessary for the successful application of the method in one and two dimensions are discussed.
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