Analytical and numerical solutions of the Local Inertial Equations

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Neglecting the convective terms in the Saint-Venant Equations (SVE) in flood hydrodynamic modelling can be done without a loss in accuracy of the simulation results. In this case the Local Inertial Equations (LInE) are obtained. Herein we present two analytical solutions for the Local Inertial Equations. The first is the classical instantaneous Dam-Break Problem and the second a steady state solution over a bump. These solutions are compared with two numerical schemes, namely the first order Roe scheme and the second order MacCormack scheme. Comparison between analytical and numerical results shows that the numerical schemes and the analytical solution converge to a unique solution. Furthermore, by neglecting the convective terms the original numerical schemes remain stable without the need for adding entropy correction, artificial viscosity or special initial conditions, as in the case of the full SVE.This research is partially funded by the FCT (Portuguese Foundation for Science and Technology) through the Doctoral Grant SFRH/BD/81869/2011 financed through the POPH/FSE program (Programa Operacional Potencial Humano/Fundo Social Europeu). This study had the support of the Portuguese Foundation for Science and Technology (FCT) Project UID/MAR/04292/2013