Boundary Conditions.

The physical boundary is partitioned in two sets: one closed, typically the coast, the other open, this is a virtual boundary delimiting the domain of investigation.

Boundary conditions employed in the mathematical model are of four kinds (Agoshkov et al., 1994):

1.

At coastline, zero normal velocity.

2.

Normal velocity is prescribed at boundaries modeling inflow from rivers.

3.

Surface elevation is prescribed in forced open boundaries, modeling a wave that enters the computational domain.

4.

Open boundary condition to simulate tidal surges that leave the computational domain (Roed & Cooper, 1987). The criterion used in this development is a variation of the Sommerfeld radiation condition (3.6).

$$\eta _t+c^x\eta _x+c^y\eta _y=0$$ (6.6)

Here $\overrightarrow{c} =(c^x,c^y)$ , $\left\vert \overrightarrow{c}\right\vert =% \sqrt{gH}$ , is the wave celerity. The wave at this boundary has the same direction as the water velocity and a heading that lets the surges leave the computational domain.