Brief Analysis of Shallow Water Equations Suitability to Numerically Simulate Supercritical Flow in Sharp Bends

Abstract

This work deals with the suitability of two-dimensional shallow water equations for the numerical simulation of supercritical free surface flows in bends, when the usual hypothesis of small width/curvature radius ratio does not hold. Here, a very reliable and accurate finite-volume, Godunov-type scheme is adopted for the numerical integration of the governing equations. Comparison with a selected set of experimental laboratory data and asymptotic analytical solutions shows that several aspects concerning the physics of the phenomenon are well reproduced, such as the blocking of the stream when the Froude number of the undisturbed flow is not large enough and the bend is sufficiently sharp, while maximum water depth in the bend is systematically underestimated.