Geoscience Reference
In-Depth Information
The performance of the method of Ying et al . is demonstrated in the simulation of
the previous dam-break flow cases shown in Figs. 9.6 and 9.7. The computational time
step is 0.6 and 0.3 s for the wet- and dry-bed cases, respectively. The Ying et al . scheme
and the central difference scheme for water surface gradient are used, i.e., either the
weighting factors w 1 and w 2 are determined with Eq. (9.56) or both are set as 0.5.
Fig. 9.8 compares the numerical and analytical solutions at 30 s after dam failure. The
Ying et al . scheme for water surface gradient provides better results than the central
difference scheme.
The method of Ying et al . is only first-order accurate, but it is simple and robust.
Extension of it to the solution of the 2-D problem (9.5) can be found in Ying and
Wang (2004).
Figure 9.8 Dam-break waves at 30 s simulated using first-order upwind flux scheme with various
schemes for water surface gradient.
9.1.6 Stability and accuracy of explicit and implicit
schemes
The aforementioned central difference scheme with artificial diffusion fluxes, approx-
imate Riemann solvers, TVD schemes, and upwind flux schemes are built in explicit
algorithms, and thus, the time step should be limited to satisfy the Courant-
Friedrichs-Lewy (CFL) stability condition. In general, the CFL condition for the 1-D
Search WWH ::




Custom Search