Enabling the MacCormack original scheme to perform dam-break flow by fitting a smoothed initial condition on a fixed non-uniform grid

摘要

In an idealized dam break incident a wave front and a depression wave starts to propagate downstream and upstream of the dam respectively. Due to the high frequencies originated near discontinuities the original MacCormack scheme produces strong oscillations near the wave front compromising the results accuracy. The objective is to enable classical schemes, such as the MacCormack, to produce accurate results free of oscillations. The developed methodology uses a variable space discretization allied with a smoothing of the initial condition. A typical dam-break case is setup for testing it and a good agreement between numerical and analytical results is found.