Mass-conserving method of characteristics for streamflow modeling

A robust numerical model is presented for the computation of unsteady streamflow on steep river slopes. The one-dimensional model uses the method of characteristics on a specified space-time grid to solve the Saint-Venant equations. An additional continuity equation requirement on each space-time element provides greatly improved conservation of mass over traditional implementations of the method of characteristics on a fixed grid. The space-time geometry of the problem is described in a finite element setting. Hermite interpolation of channel parameters is used to avoid numerical difficulties that may occur with steep slopes due to discontinuities in the derivatives of data such as channel top width. Manning's equation for friction slope can be modified by a factor to make the slope more appropriate for steep rivers. The standard Manning's friction slope can also be used, if preferred. The computer model is not restricted to steep slopes, and applies as well to gently sloping streams. Two numerical examples support the mathematical approach and computational algorithm.