Numerical study of shallow-water equations using three explicit schemes - application to dam break flood wave

Abstract

The numerical method to solve dam break problem on regular bathymetry was developed. Two cases of dam break wave propagation on wet and dry bottoms were selected to verify the numerical model elaborated. Three numerical schemes of Lax-Friedrichs, Adams-Bashforth and Adams-Bashforth-Adams-Moulton are applied to simulate this phenomenon using the 1D Saint-Venant equations. An artificial viscosity is added to these numerical schemes to provide stability and reduce numerical diffusion. This viscosity makes the numerical scheme robust (very powerful) for the simulation of this phenomenon. The results obtained show that these developed models are able to simulate dam break wave propagation process. The relative error in the L1 norm between the computed results and analytical solutions is calculated. The L1 norm indicates that the Adams-Bashforth-Adams-Moulton scheme has better accuracy than the other two schemes. It is shown that the technique used is simple, accurate, robust and stable for the simulation of the dam break wave propagation on wet and dry bed conditions.