Using Inverse Laplace Transform for the Solution of a Flood Routing Problem

The inverse Laplace transform is of great importance in mathematical sciences when an analytical solution exists in Laplace domain. A new solution of the linearized St. Venant equations (LSVE) has been obtained for flood routing. The LSVE has been previously used by many researchers. In the formulation, the linearized form of the Manning formula is combined with the LSVE to get a Laplace transformable, simplified set of equations. There are different simplifications in the literature to get an analytical solution in time domain, not applicable to complicated form of equations. The results of discharge and depth predictions show that improved De Hoog algorithm provides a solution with very small error, when applied to the LSVE. Moreover, the model solution is compared against the numerical solution of the LSVE using the well-known Preissmann implicit finite difference scheme. The model outputs indicate a very good agreement with the numerical solution. It is notable that in the results reported by Litrico and Fromion [1], the LSVE was limited to maximum variation of 5% in discharge, however in the current paper the range of the variation is reached to 50% of the initial discharge.