Discussion of 'Modeling 3D Supercritical Flow with Extended Shallow-Water Approach' by Susanne Krueger and Peter Rutschmann

摘要

The authors present a very interesting mathematical model that calculates three-dimensional (3D) supercritical flows. Turbulence is included via the use of an eddy viscosity (called in the paper as "global diffusion factor"), which is constant over the entire domain. The model employs the extended shallow water equations (ESW), which are modifications of the classical shallow-water equations (CSW) taking into account nonhydrostatic pressure distribution and vertical momentum. The ESW are solved using (a) the FEMTOOL (Rutschmann 1993); and (b) a low-order upwind Galerkin/least-squares discretization procedure (Hughes et al. 1989). The authors implement a water-depth limitation in regions with very small water depths to avoid numerical difficulties associated with alternating wet-drying; moreover, they introduce a numerical diffusion coefficient, which is used in steep surface gradients, to avoid premature program termination due to steep water depth gradients in regions with wave breaking.