Numerical Study on Rapidly Varied Unsteady Free-Surface Flows

Numerical analysis of unsteady flows in an open channel by the modified MAC method (I)

Abstract

It is important to clarify the characteristics of free surface flows which change rapidly, and it is necessary to understand the internal mechanism and internal structure of these flows.
The MAC (Marker-and-Cell) method is one of the numerical techniques for handling time dependent variation of free surface and shows the internal structure of these flows. In this paper, the SMAC (Simplified MAC) method is modified and employed. Two-dimensional numerical simulation of the Dam Break Wave (one typical example of those flows) is performed.
The Dam Break Wave is considered as a flow brought on by a sudden full opening of the gate. The numerical results are compared with experimental and theoreticalresults.
The config uration of the free surface in upstream region of the gate is convex to upward, and so on (Figs. 8-10, 13, 17), and this is in good agreement with experimental results.
The internal structure of this flow, velocity distribution and pressure distribution are shown in Figs. 14-15.
It seems that the good agreement between the results of calculation and that of the experiments and the theoretical results shows the validity of the numerical method employed in this paper.