Nonlinear Shallow Water Wave Propagation in a Variable-Depth Channel

Resumo

The nonlinear Shallow Water Equations (SWE) for a homogeneous fluid (see, e.g., Wu et al. [1], Struve et al. [2]) is solved numerically by the Finite Element Method (FEM). Advective, hydrostatic pressure, atmospheric pressure and viscosity effects are included in the numerical solution. The baroclinic effect, Coriolis force and the wind action are disregarded in this simulation. To minimize the residual in each element, the Weighted Residuals (Galerkin) Method is used. The reflective (natural) boundary condition was implemented in order to simulate the rigid wall on right side of the channel (tank). The numerical code is written in Fortran 95 language and the Octave graphical interface is used to analyze the results. The GMSH mesh generator (v. 4.8.4) is used to represent the continuous domain by a set of discrete points that are grouped to form a non-uniform mesh of triangular elements. The numerical results of wave generation by a piston-type wavemaker (Goring [3], Whitham [4]) are compared with experimental results (Briggs et al. [5]) for the generation of solitary waves in a variable depth channel. The numerical results are in good agreement with those reported in the literature (Silva et al. [6], Takagi [7], Gardarsson [8]).