Treatment of Natural Geometry in Finite Volume River Flow Computations

A method is proposed for the treatment of irregular bathymetry in one-dimensional finite volume computations of open-channel flow. The strategy adopted is based on a reformulation of the Saint-Venant equations. In contrast with the usual treatment of topography effects as source terms, the method accounts for slope and nonprismaticity by modifying the momentum flux. This makes it possible to precisely balance the hydrostatic pressure contributions associated with variations in valley geometry. The characteristic method is applied to the revised equations, yielding topographic corrections to the numerical fluxes of an upwind scheme. Further adaptations endow the scheme with an ability to capture transcritical sections and wetting fronts in channels of abrupt topography. To test the approach, the scheme is first applied to idealized benchmark problems. The method is then used to route a severe flood through a complex river system: the Tanshui in Northern Taiwan. Computational results compare favorably with gauge records. Discrepancies in water stage represent no more than a fraction of the magnitude of typical bathymetry variations.