Finite-difference TVD scheme for computation of dam-break problems

A second-order hybrid type of total variation diminishing (TVD) finite-diff erence scheme is investigated for solving dam-break problems. The scheme is based upon the first-order upwind scheme and the second-order Lax-Wendroff scheme, together with the one-parameter limiter or two-parameter limiter. A comparative study of the scheme with different limiters applied to the Sa int Venant equations for 1D dam-break waves in wet bed and dry bed cases sh ows some differences in numerical performance. An optimum-selected limiter is obtained. The present scheme is extended to the 2D shallow water equatio ns by using an operator splitting technique, which is validated by comparin g the present results with the published results, and good agreement is ach ieved in the case of a partial dam-break simulation. Predictions of complex dam-break bores, including the reflection and interactions for 1D problems and the diffraction with a rectangular cylinder barrier for a 2D problem, are further implemented. The effects of bed slope, bottom friction, and dep th ratio of tailwater/reservoir are discussed simultaneously.