The goal of this verification test to asses the model performance in simulating nonlinear runup/rundown over a plane slopt. Carrier et al. (2003) presented an analytical solution to the nonlinear shallow water equations over a plane slope for several initial wave forms. Here the analytical solution for a the initial wave form given by leading-depression N-wave is used.
The bed has a constant slope of 1/10 with the initial shoreline located at x=0. Figure 1 shows the initial water level (is given by a leading depression N-wave (characteristic of the waves caused by submarine landslides). The initial current velocity is equal to zero everywhere.
The computational grid has a 3 m resolution for x<300 and increases to 10 m with an aspect ratio of 1.05. The general model parameters used in the simulation are shown in Table 1.
Table 1. Model Parameters
|Time step||0.1 s|
|Ramp period||0.0 s|
|Drying depth||0.01 m|
Figure 2 shows a comparison of computed and analytical water surface elevations near the shoreline at 4 different time steps. The goodness of fit statistics are shown in Table 2.
Table 2. Goodness of Fit Statistics
|Time, s||RRMSE, %||RMAE, %||R^2||Bias, m|
- For a definition of the goodness of fit statistics see Goodness of fit statistics.
A comparison of the calculated and analytical shoreline position are shown in Figure 3.
- Carrier, G., Wu, T.T., and Yeh, H. (2003). "Tsunami runup and draw-down on a plane beach", Journal of Fluid Mechanics, 475, 79-99.