Numerical modeling of flows in open channels by a semi-implicit finite volume scheme

Abstract

Abstract Canals and sewers are part of the structure of our cities. Flow modelling in these channels allows us to prevent and anticipate most problems and disasters that may occur. This work focuses on the modelisation of flows in open channels with variable beds and geometries. The section is rectangular or trapezoidal, variable in the direction of the length and the regime is subcritical or supercritical. The flow is governed by the equations of Saint-Venant and the resolution is carried out by the semi-implicit scheme whose use allows a wide time step offering a saving in CPU time, however, handling and inverting large matrices is very expensive in CPU time. The source term is processed by the upwind scheme of Roe-Vazquez in order to verify the C-property. The application to tests whose analytical solution is known shows a very good agreement between the numerical and theoretical solutions.