ABSTRACT
Modeling the Saint-Venant equations in natural river systems is challenging because channel variability results in non-smooth geometric gradients that can cause solution divergence. We propose new forms of the Saint-Venant equations for addressing this problem using both finite-volume and finite-difference formulations. A recently-developed exact mathematical transformation is used to represent non-smooth channel geometry with a smooth approximating reference slope while preserving the true channel cross-sectional area, perimeter, and gradients. We apply this approach to both the traditional Cunge-Liggett differential form of the Saint-Venant equations and a recently-developed conservative finite-volume form. The latter allows the pressure interaction of the sloping channel bottom and the sloping free surface to be handled as a numerical quadrature term that can be approximated with a polynomial.
