Abstract:
Wave-structure interaction and wave propagation on complex topography are very
important in Coastal Engineering. They involve phenomena that combine reflection, shoaling,
refraction and diffraction that generate harmonics with complex energy transfers. Over the past
decades, many numerical models have been developed to deal with these problems. Due to the large
horizontal dimensions of the region under study, the numerical solutions of the Navier-Stokes
equations have high computational costs to determine the three-dimensional velocity and pressure
fields, besides the free surface position. However, when flow separation, vortex or turbulence
phenomena are involved, Reynolds-averaged Navier-Stokes models provide more accurate results.
The objective of this paper is to apply the FLUINCO model (P. Teixeira and C. Fortes, Rev. Int. Mét.
Num. Cálc. Dis. Ing., 25(2):313-336 (2009)) to test cases of wave propagation in channels. FLUINCO
employs the two step semi-implicit Taylor-Galerkin fractional method to discretize the Navier-Stokes
equations in time and space. The code adopts linear tetrahedral elements and the arbitrary Lagrangian-
Eulerian formulation to enable the solution of problems concerning the free surface motion. A
smoothing procedure is applied to the mesh velocity distribution to minimize element distortion,
considering the velocities of each node belonging to the boundary surface. The first application is the
wave propagation in a channel of constant depth. The energy spectrum, pressure and velocity fields
produced by the numerical model are compared with linear and nonlinear wave theories. The second
case deals with the wave propagation over the trapezoidal submerged breakwaters. Two types of
breakwater slopes are studied: the first with upstream and downstream slopes of 1:20 and 1:10,
respectively; and the second with both 1:2 slopes. The results of the surface elevation and the energy
spectrum at various points in the field as well as the pressure and velocity fields for each breakwater
geometry are presented. In the last case, vortices near the upstream slope, that increase nonlinear
effects, are found. Finally, the wave propagation over a submerged horizontal cylinder is analyzed and
these results are compared with experimental ones. The flow near the cylinder, the free surface and
the velocity profiles on several gauges are analyzed.
