The weakly and fully nonlinear Boussinesq equations (Equations 4-9) are

solved in the time-domain using a finite-difference method. The computational

domain is discretized as a rectangular grid with grid sizes ∆*x *and ∆*y*, in the *x *and

grid points in a staggered manner as shown in Figure 3. The water depth and

surface elevation are defined at grid points (*i,j*), while the velocities are defined

half a grid point on either side of the elevation grid points. The external boun-

daries of the computational domain correspond to velocity grid points.

Figure 3.

Computational grid for finite difference scheme

12

Chapter 3 Numerical Solution

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