Evaluating shallow water assumptions in dam-break flows

It has become common practice to model dam-break floods with shallow water equations. Shocks in the flow can be reproduced in the form of discontinuities in the weak solution. Strictly speaking, the underlying assumptions behind the shallow water equations, such as gradual variation, small vertical velocity component and hydrostatic pressure distribution, are invalid close to the shocks. In an attempt to examine the accuracies/inaccuracies of the shallow water equations in modelling fast-varying flows, solutions to the shallow water equations are compared with laboratory measurements and solutions to the Navier–Stokes equations. The shallow water equations' predictions are made by using an extensively verified total variation diminishing-MacCormack scheme, while the Navier–Stokes equations are solved by using a smoothed particle hydrodynamics model. The propagations of the flood wave due to the entire and partial dam-breaks are simulated. The smoothed particle hydrodynamics model has shown the capability of reproducing complex flows involving highly distorted free surfaces. Apart from being unable to simulate the complex water surface geometry, the shallow water equations model tends to overestimate the propagation speed and steepness of waves when the water column is slender or when multiple waves interfere with each other.