Hodges B.RCHENG-WEI YULiu F.2022-11-112022-11-112020https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117395724&partnerID=40&md5=2e95549f8923bbd0e6f94fd3daa211c2https://scholars.lib.ntu.edu.tw/handle/123456789/624593Modeling 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, LondonHydraulics; Stream flow; Channel geometry; Cross sectional area; Differential forms; Finite-volume; Natural river; New approaches; New forms; River systems; Saint Venant equation; Smooth channel; Riversconference paper2-s2.0-85117395724