A well‐balanced FV scheme for compound channels with complex geometry and movable bed

Abstract

This work focuses on the implementation of a Shallow Water-Exner model for compound natural channels with complex geometry and movable bed within the finite volume framework. The model is devised for compound channels modeling: cross-section overbanks are treated with fixed bed conditions, while the main channel is left free to modify its morphology. A capacitive approach is used for bed load transport modeling, in which the solid flow rates are estimated with bed load transport formulas. The model equations pose some numerical issues in the case of natural channels, where bed load transport may occur for both subcritical and supercritical flows and geometry varies in space. An explicit path-conservative scheme, designed to overcome all these issues, is presented in the paper. The scheme solves liquid and solid phases dynamics in a coupled manner, in order to correctly model near critical currents/channel interactions and is well-balanced, that is able to properly reproduce steady states. The Roe and Osher Riemann solvers are implemented, so as to take into account the spatial geometry variations of natural channels. The scheme reaches up to second-order accuracy. Validation is performed with fixed and movable bed test cases whose analytical solution is known, and with flume experimental data. An application of the model to a real case study is also shown.