2D Finite Volume Numerical Modeling of Free Surface Flows with Topography

Abstract

In this thesis a finite-volume MUSCL-type scheme for the numerical solution of inhomogeneous SWE is presented. The novel aspect is data reconstruction: the scheme, named WSDGM (Weighted Surface-Depth Gradient Method), computes intercell water depths performing a weighted average of DGM and SGM reconstructions, in which the weight function depends on the local Froude number. This combination makes WSDGM capable of performing a robust tracking of wet/dry fronts and, together with an unsplit centered discretization of the bed slope source term, of exactly maintaining the static condition on non-flat topographies (C-property). Moreover, a numerical procedure performing a correction of the numerical fluxes in the computational cells with water depth smaller than a fixed tolerance enables a drastic reduction of the mass error in the presence of wetting and drying fronts. The effectiveness and robustness of the proposed scheme were assessed by comparing numerical results with the analytical and reference solutions of a set of test cases. Finally, to check the numerical model to field-scale applications, the results of two hypothetical dam-break events are reported.