Analytical and numerical solutions of the Local Inertial Equations |
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Institution: | 1. CIMAT, Center of Research in Mathematics, Guanajuato, Gto 36000, Mexico;2. ITESM, Monterrey Institute of Technology and Higher Education, Zapopan, Jalisco 45138, Mexico |
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Abstract: | 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. |
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Keywords: | Numerical models Analytical solutions Local Inertial Equations Dam-Break |
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