Discussion of 'Case Study: Malpasset Dam-Break Simulation Using a Two-Dimensional Finite Volume Method' by Alessandro Valiani, Valerio Caleffi, and Andrea Zanni

摘要

The authors should be congratulated for their interesting paper, for both the lucidity and completeness of the approach proposed and for the remarkable application to the case of the Malpasset dam break. Models like those proposed by the authors are really important for forecasting purposes, and the control of their reliability, such as the one demonstrated in the paper, is absolutely necessary to guarantee their applicability in the real world. The discussers are setting up a two-dimensional finite volume model (2D-UFM model, Barbiero et al. 2002; Pianese and Barbiero 2003) for the study of a number of water- and debris-flow processes as well as the impact, dissipation, and stoppage phenomena that could take place because of the presence of structures. The approach used by the discussers is quite similar to that proposed by the authors, as well as some of the considered study cases. Thus, the discussers decided to test their model by considering the data relating to the Malpasset dam break case study. Herein is a discussion with the results obtained by the application, to real cases, of models such as those proposed by the authors and discussers on the relative importance of improvements that could be introduced into the models to better reproduce the topography and boundaries of the study area. The approach used by the discussers differs from the one applied by the authors in several ways, such as (1) the use of triangular cells, instead of square ones, helps to better reproduce the boundaries (by means of an algorithm based on the Delaunay method, given by Rebay 1993) and provides a faster and more precise calculation of the bottom slopes in any direction; (2) the bottom elevations at any node of the mesh are determined by an interpolation procedure using a powerful commercial software (SURFER 8.0) that, starting from known bed elevations corresponding to certain points, generates (by a number of techniques as kriging, triangulation, etc.) 3D surfaces; (3) the software takes into account the real effects of the slopes, according to the approach proposed by Yen (1975); (4) the solutions of the Riemann problem are obtained by choosing between two approximate solvers: the Harten, Lax and van Leer method (Toro 1997) and the Osher method, according to the P variant (Hemker and Spekreijse 1986); (5) the simulation of dry bed conditions is accomplished by the HLL method case by a Kinematic modeling of the wetting and drying phenomena because the hydraulic depth is less than a H_(TOL_1) value in the case of the O-P method, and referring to variable bed conditions that go from entirely dry to partially wet and entirely wet and considering two limit values, H_(TOL_1) and H_(TOL_2) (Zhao et al. 1994); (6) at the present, the model does not include a procedure for the reconstruction of the trends of corresponding variables at cell interfaces (such as the MUSCL technique considered by the authors), methods to damp oscillations (such as Roe's approximate Jacobian, TVD, or ENO schemes), or techniques for the source terms treatment.