New approaches to solving the Saint-Venant equations
Journal
River Flow 2020 - Proceedings of the 10th Conference on Fluvial Hydraulics
Pages
1089-1096
Date Issued
2020
Author(s)
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. © 2020 Taylor & Francis Group, London
Other Subjects
Hydraulics; Stream flow; Channel geometry; Cross sectional area; Differential forms; Finite-volume; Natural river; New approaches; New forms; River systems; Saint Venant equation; Smooth channel; Rivers
Type
conference paper