Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flow

Abstract

A revision of some well-known discretization techniques for the numerical boundary conditions in 1D shallow-water flow models is presented. More recent options are also considered in the search for a fully conservative technique that is able to preserve the good properties of a conservative scheme used for the interior points. Two conservative numerical schemes are used as representatives of the families of explicit and implicit numerical methods. The implementation of the different boundary options to these schemes is compared by means of the simulation of several test cases with exact solution. The schemes with the global conservation boundary discretization are applied to the simulation of a real river flood wave leading to very satisfactory results.