Geoscience Reference
In-Depth Information
In order to solve the mathematical model of free surface water flow (
3
), a
numerical method of partial difference equations integration has to be implemen-
ted. To integrate the model in space, the finite volume method (LeVeque
2002
) was
applied. This method requires to calculate the fluxes of mass and momentum
through the computational cells (volumes) interfaces. They were computed using
the Roe scheme (Roe
1981
). Detailed description of the method is available in the
literature (Toro
1997
); therefore, it is not presented in this chapter. The solution of
(
3
) must be completed with time integration scheme. The two-step explicit scheme
of finite difference method is used in solution algorithm. The computational code
for numerical simulation of the flash floods was prepared at the Hydroengineering
Department of Gda
´
sk University of Technology (Szydłowski
2007
).
4 Flood Numerical Simulation
The geometry of potential flood region is presented in Fig.
4
. It was covered with
the unstructured triangular mesh composed of 12,463 elements. The mesh was
locally refined along the reservoir embankments to better represent the relief of the
floodplain and complex structure of the flow near the breach. In this region, the
lengths of the element sides were equal to 5 m. They were increasing up to 50 m
with the distance from the reservoir embankments. The additional mesh refinement
was applied along an expected flood path.
The reservoir was excluded from the computational domain. The boundary
of the computational domain along the reservoir embankment (except for the
breach) was assumed closed. The other boundaries were treated as the open ones.
Initially, at the beginning of the flood simulation, the surface of the floodplain was
assumed dry. At the broken dike segment, the hydrograph (Fig.
3
) was assumed as a
boundary condition. The calculations were carried out with the time step
D
t
¼
0.1 s
and the total simulation time was equal to 1.5 h.
Fig. 4 Geometry of flow area and numerical mesh
