A VFRoe scheme for 1D shallow water flows : wetting and drying simulation

2006/09/20 by Bello, Abdou Wahidi
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.cs/0609114

Abstract

A finite-volume method for the one-dimensional shallow-water equations including topographic source terms is presented. Exploiting an original idea by Leroux, the system of partial-differential equations is completed by a trivial equation for the bathymetry. By applying a change of variable, the system is given a celerity-speed formulation, and linearized. As a result, an approximate Riemann solver preserving the positivity of the celerity can be constructed, permitting wetting and drying flow simulations to be performed. Finally, the simulation of numerical test cases is presented.

Related

• A simple numerical scheme for the 2D shallow-water system
• A combined finite volume - finite element scheme for a dispersive shallow water system
• Survey of Mathematical Models of and Numerical Methods for Fluid Dynamics Water Engineering
• A continuous/discontinuous Galerkin solution of the shallow water equations with dynamic viscosity, high-order wetting and drying, and implicit time integration
• Bathymetry and friction estimation from transient velocity data for 1D\n shallow water flows in open channels with varying width