Simulation of dam-break fluvial processes - Computational River Dynamics - page 362

problem is

|+ gh

| q / h

t < 1 (9.57)

x

and for the 2-D problem is

gh gh

| U x |+

+ |

U y |+

t < 1 (9.58)

x y

However, the stability of each numerical scheme also may rely on its own formu-
lation, and the longest time step allowed for a stable solution varies among different
schemes.
To relax the restriction on time step imposed by the CFL conditions, Molls and
Chaudhry (1995) adopted the ADI method and Delis et al . (2000) established implicit
TVD schemes for 1-D St. Venant equations. It has been found that longer time steps can
be used in implicit algorithms, and the computational cost may be reduced. However,
implicit schemes may induce numerical diffusion. This is demonstrated in the following
example using the SIMPLEC algorithm

Figure 9.9 Dam-break waves at 30 s simulated using SIMPLEC.