Geoscience Reference
In-Depth Information
The SIMPLEC algorithm described in Section 6.1.3.1 is developed primarily to
simulate common open-channel flows, but its superior numerical stability makes it
feasible for simulation of dam-break flow. This is tested by simulating the previ-
ous wet- and dry-bed cases shown in Figs. 9.6 and 9.7. To investigate the effect
of time step on the simulation results, the time step is set as 2.0 and 0.5 s for
the wet-bed case and 0.75 and 0.15 s for the dry-bed case. The hybrid (Spalding,
1972) and SOUCUP (Zhu and Rodi, 1991) schemes are used for the convection
terms. The results are shown in Fig. 9.9. The model reproduces reasonably well
the upstream negative wave and downstream positive wave. The hybrid scheme pro-
duces slightly larger errors in water level than the SOUCUP scheme. One can see
that a smaller time step gives a better prediction. As the time step increases, the
wave front becomes less sharp. This is due to numerical diffusion, which is partic-
ularly significant near regions with sharp gradients. This was also observed in the
implicit method of Delis
et al
. (2000). There is a trade-off between the time step
length (i.e., computational efficiency) and numerical accuracy when implicit algo-
rithms are used in the simulation of dam-break flow where discontinuities and sharp
gradients exist.
9.2 SIMULATION OF DAM-BREAK FLOW
OVER MOVABLE BEDS
Simulation of dam-break flow over movable beds is much more challenging than that
over fixed beds. One of the problems encountered in the movable-bed case is that
the sediment concentration is so high and the bed varies so rapidly that the effects of
sediment transport and bed change on the flow cannot be ignored. Another problem
is that the sediment transport in the higher flow regime, such as dam-break flow, is
little understood, and the existing sediment transport formulas may not be applicable.
Ferreira and Leal (1998), Fraccarollo and Armanini (1998), and Yang andGreimann
(1999) established movable-bed dam-break flow models. However, some of these
models ignore the effects of sediment transport and bed change on the flow, and
some use the assumption of local equilibrium sediment transport that is no longer
valid in the case of dam-break flow. Fraccarollo and Capart (2002) proposed a
two-layer model of movable-bed dam-break flow in which the clear water in the
upper layer and the mixture of sediment and water in the lower layer are sim-
ulated separately. The applicability of this two-layer model is limited because a
constant sediment concentration is assumed in the lower layer. Capart and Young
(1998), Cao
et al
. (2004), and Wu and Wang (2007) developed more advanced
models for dam-break flow over movable beds, considering the non-equilibrium
sediment transport and the effects of sediment concentration and bed change on
the flow. However, the sediment exchange model proposed by Capart and Young
does not consider the effect of sediment size, and thus, its applicability is restricted.
The model of Cao
et al
. (2004) simulates only the suspended-load transport and
needs to be tested quantitatively. Wu and Wang's model simulates the total-load
transport and has been verified using available experimental data. It is introduced
below.
