RESULTS OF NUMERICAL EXPERIMENTS
Using this computational method a number of computational experiments of tsunami runup on a shore of an arbitrary profile are carried out. The main goal of these computations was testing of this algorithm using results of other methods and investigation of the runup height dependence from the shore profile.
The first series of test experiments was carried out for the uniformly sloping shore with following parameters:
Spatial step of the grid: 
dx = 10 meters. 
Initial number of computational gridpoints: 
M = 400 
Time step : 
dt = 0.2 seconds 
Length of an incident wave (expression 3): 
B = 0.05 
Initial wave height: 
h = 2 meters 
The wave was generated at the distance of 4 kilometers off the shore. The bottom profile was as following: from the wateredge point the bottom has the constant inclination angle (tg α=0.1) and increase linearly till the depth 100 m. Then, the depth is not varying until the left boundary. Table 1 shows the runup heights of generated waves at different beach slopes:
Table 1. Calculated wave runup height according to the beach slope angle.
Beach slope angle tg(α) 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
Runup height 
19.5 
19.3 
18.9 
18.5 
18.1 
17.8 
17.5 
17.3 
17.1 
16.9 

During the way to the coast the wave height increases up to 8 meters. From
the table it is visible, that increasing of declination of a shore causes decreasing of the wave runup
height, which corresponds to the results obtained earlier with the help of analytical ( Pelinovsky,
1982, 1985) and numerical methods ( Marchuk, 1982).
In Figure 3 the wave profile at the moment of maximum runup is shown.
Figure 3. The moment of highest runup of a wave to the uniform slope
Now we shall consider tsunami wave runup on a shore with a more complicated profile. The second series of numerical experiments is carried out in order to investigate correlations between wave runup height and shore profiles of submerging area. In this case the submerging area of the shore (up to 25 meters above mean sea level) has the profile, which is defined by the following expression:
Here the distance r measured from the initial wateredge point to the right, and r_{0}  is the width of a shore area with varied declination (in this series of calculations it was equal to 250 meters). All remaining parameters were the same, as in the previous case. In this series of computations the wave height near the shore was equal to 7.6 m. As the result of computations with the positive values of parameter C the following table was obtained:
Table 2. Runup heights for positive curvature parameter values
Curvature parameter C 
0.0 
1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
Runup height 
23.067 
23.086 
23.132 
23.73 
23.86 
23.54 
23.68 
23.63 

The shore and the water surface profile when the curvature parameter value is equal to 4 are shown in the Figure 4.
Figure 4. Wave runup on a shore with the positive curvature parameter (C
= 4)
Results of computations with the negative values of the curvature parameter C are shown in the Table 3.
Table 3. Runup heights for negative curvature parameter values
Curvature parameter C 
1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
Runup height 
22.58 
22.82 
22.40 
22.37 
21.88 
20.86 

The shore and the water surface profile when the curvature parameter value is equal to 6, are shown in Figure 5.
Figure 5. Wave runup on a shore with the negative curvature parameter (C
= 6)
From Tables 2 and 3 it is seen that the maximum runup height of the wave with
given initial parameters is observed when parameter C is equal to +4.
