One-Dimensional Dam-Break Solutions for Variable Width Channels

In modeling dam-break floods in natural channels, the practicing engineer must decide whether to use a one-dimensional (1D) or a two-dimensional (2D) numerical model. Here in the examination of what might be considered a 2D problem, it is clearly illustrated that a 1D formulation provides an excellent solution. The solution is based on a formulation of the St. Venant equations developed for rectangular channels of varying widths, which are applied to the experimental dam-break study conducted in a converging-diverging flume. Numerical solutions based on a conservation formulation solved with the characteristic dissipative Galerkin (CDG) finite-element method are compared to results obtained with a conventional nonconservation formulation, solved by the “box” (four-point implicit) finite-difference method. For subcritical dam-break problems, it is shown that the quality of the result does not depend upon the particular numerical solution technique used. Although the four-point implicit scheme was unable to provide solutions in tests where both subcritical and supercritical flow occurred, the CDG results shows that any conservative, shock capturing 1D scheme would work well on this type of problem.