Analytical Solution of the Classical Dam-Break Problem for the Gravity Wave–Model Equations

Abstract

Saint-Venant Equations (SVE) are often simplified for the sake of practicality, faster computational times, or physical representation. The Gravity Wave Model (GWM), or Local Inertial Equations, is a simplification of the SVE whereby the convective terms are neglected. The aim of this work is to present an analytical solution for the dam-break problem based on the GWM set of equations without source terms using the method of characteristics (MOC) and compare it with the analytical solution of SVE. The formulas for the depth and velocity are derived and explained along with the wave propagation characteristics. Conclusions are drawn about the propagation and analytical solution.