Criteria for the choice of flood-routing methods in natural channels

Abstract

The Saint-Venant equations are used to describe river waves. Generally, for flood routing in rivers, the Saint-Venant system is reduced to the diffusive wave equation which can be resolved using finite-difference algorithms. The choice of a numerical method, and of the space and time steps to be retained, depends essentially on the form of flood hydrographs and the hydraulic properties of the river. This paper investigates these areas; two sets of criteria are propossed, the first to define parameter ranges representing each wave type and then, in the particular case of the diffusive wave model, to define criteria for the choice of numerical algorithm and appropriate space and time steps. The first analysis was based on the concept that river wave behaviour is determined by the balance between friction and inertia. The conclusions relate to the magnitude of temporal characteristics of flood waves, expressed as a function of the Froude number of the steady uniform flow and a dimensionless wave number of the unsteady component of the motion. The second part discussed questions related to the diffusive wave problem and to numerical instabilities. A technique is proposed to guide the user in the choice of the computational algorithm and specifies the error introduced by numerical methods. The technique was applied to flood-routing simulation for the Loire river in France. In this case, two finite-difference algorithms were compared to the exact solution given by the analytical method. Comparisons between results show the efficiency of the technique to optimise the choice of the finite-difference method and the adequate space and time steps.