| Abstract: | Generally, the diffusive wave equation, obtained by neglecting the acceleration terms in the Saint-Venant equations, is used in flood routing in rivers. Methods based on the finite-difference discretization techniques are often used to calculate discharges at each time step. A modified form of the diffusive wave equation has been developed and new resolution algorithms proposed which are better adapted to flood routing along a complex river network. The two parameters of the equation, celerity and diffusivity, can then be taken as functions of the discharge. The resolution algorithm allows the use of any distribution of lateral inflow in space and time. The accuracy of the new algorithms were compared with a traditional algorithm by numerical experimentation. Special attention was given to the instability caused by the inflow signal which constitutes the upstream boundary condition. For the fully diffusive wave flood routing problem, all three algorithms tested gave good results. The results also indicate that the efficiency of the new algorithms could be significantly improved if the position of the x-axis is modified by rotation. The new algorithms were applied to flood routing simulation over the Gardon d'Anduze catchment (542 km2) in southern France. |
