# Test 13

## 2-D Wave interaction with perforated breakwaters.

By Domenico Davide Meringolo, Francesco Aristodemo (

(Download full test case data files here: SPHERIC_TestCase13.zip)

## Introduction

Perforated wall-caisson breakwaters are
coastal structures widely used in harbours and port areas with the aim to dissipate incident wave energy, allowing
for safe navigation conditions during sea storms.
In recent
years, the increasing number of installation of perforated breakwaters in port
areas addressed the interest of the scientific community to a deeper
understanding of the dissipation process occurring inside the chamber of the
breakwaters and the related analysis of wave reflection. Moreover, the analysis
of the dynamic pressures at the walls is fundamental in terms of stability
analysis.

The SPH
offers a further insight for an engineering problem whose dimensioning is nowadays
essentially based on approximated empirical formulas.

## Flow phenomena

The dissipation process occurring
in the non-reflective cells of the perforated breakwater depends on the
geometrical configuration of the caisson and on the incident wave characteristics.

The fluid dynamics inside the chamber of the caisson, induced by the wave
action, is a complex phenomenon in which the pressure gradients between the
outside and the inside of the structure regulates the flow evolution.

## Geometry

Two geometries of
perforated breakwaters, characterized by a top cover plate over the free surface on an
internal chamber (see Fig. 1), are analysed. Both analyses are performed
considering water depth *d* = 0.4 m,
while *d’* = 0.2 m. The length of the
numerical wave flume is *L* = 4 m.__Breakwater
n°1__

The first
breakwater is perforated by two holes at the front face, with *B* = 0.2 m, *b’* = 0.08 m, *s* = 0.038 m,
*h* = 0.024 m, *b* = 0.096 m. The incident wave train is regular with *H* = 0.08 m and *T* = 1.2 s.__Breakwater
n°2__

The second
breakwater is perforated by three holes at the front face, with *B* = 0.15 m, *b’* = 0.16 m, *s* = 0.038 m,
*h* = 0.024 m, *b* = 0.096 m. The incident wave train is regular with *H* = 0.1 m and *T* = 1 s.

Figure 1. Breakwaters sketch (Figure only).

## Boundary
conditions

No-slip solid boundary
conditions are enforced. The wave generation is obtained by implementing the
left wall of the wave flume with a sinusoidal time law.

## Initial
conditions

The fluid particles are
initialized with a hydrostatic pressure distribution, while the initial
velocity field is set equal to zero everywhere in the domain.

## Discretisation

A spatial resolution *d**x* = 0.0035 m is adopted. The
specification of the initial position of the fluid and solid particles is given
in the files:

“Initial_particles_distribution_breakwater_n1.dat”

“Initial_particles_distribution_breakwater_n2.dat”

Column 1: X position (m)

Column 7: def = 1 for fluid particles, def = 2
for solid particles

## Results specification

Results to be returned for
this test are the spatial dynamic pressure distribution at the walls of the
breakwater (front face, front inner wall, rear inner wall). The wave considered
for the analysis is the first wave impacting on the wall (after the initial
wave if the wavemaker motion presents a transient initial law to avoid shock
waves in the channel).

The
spatial distributions of dynamic pressures at the front wall and at the
internal walls of the chamber, are analyzed when the maximum pressure induced
by the wave crest within the regular wave train appears in correspondence to
the SWL. Is noticed that the pressure peaks
at the three reference walls appear at different time instants. Their phase
shift is dependent on the wave celerity and the width of the chamber.

## Results format

The experimental result of
the spatial distribution of the dynamic pressures (obtained by Chen et al.,
2007) are presented in the files:

“Delta_P_EXPERIMENTAL_breakwater_n1.dat”

“Delta_P_EXPERIMENTAL_breakwater_n2.dat”

Column 1: Z position of the pressure gauge
(m)

The SPH results of the
spatial distribution of the dynamic pressures, measured in this case for all
the points along the depth, equispaced with a distance *d**x*, are given in the files “Delta_P_SPH_breakwater_n1.txt”
and “Delta_P_SPH_breakwater_n2.txt”. The results refer to the coupled diffusive
formulation (green line in Fig. 2, for more information see Aristodemo et al.,
2015):

Column 2: Dynamic pressure (kPa)

**Benchmark
results**

For more specification on
the benchmark results see Chen et al., 2007. For more specifications on the
numerical results see Aristodemo et al., 2015.

Figs. 2
and 3 the frames of the simulations with pressure field and velocity vectors
are shown for the case of the breakwater no. 1 and no. 2, respectively (Figures
only).

Figure 2. Frames of the simulation with pressure distribution and velocity vectors for the breakwater geometry no. 1. Left plot: wave crest at the front wall. Right plot: wave trough at the front wall.

Figure 3. Frames of the simulation with pressure distribution and velocity vectors for the breakwater geometry no. 2. Left plot: wave crest at the front wall. Right plot: wave trough at the front wall.

The
spatial distributions of dynamic pressures at the front wall and at the
internal walls of the chamber, are shown in Fig. 4 and 5. Positive dynamic
pressures are displayed on the external side of the walls and negative ones on
their internal side.

Figure 4. Spatial distribution of wave pressures at perforated breakwater no. 1: Experiments vs SPH.

Figure 5. Spatial distribution of wave pressures at perforated breakwater no. 2: Experiments vs SPH.

## SPH Publications
using this Case

- Aristodemo, F., D.D. Meringolo, P. Groenenboom, A. Lo Schiavo, P. Veltri, M. Veltri, “Assessment of dynamic pressures at vertical and perforated breakwaters through diffusive SPH schemes”.
*Mathematical Problems in Engineering*, Article ID 305028, vol. 10 pages, 2015. Meringolo, D.D., 2016. Weakly-Compressible SPH Modeling of Fluid-Structure Interaction Problems (Ph.D. thesis). Università della Calabria, Cosenza, Italy.

**If you have published results for this case, please email the webmaster
to have your papers added.**

## References

- Chen, X. F., Y. C. Li, and B. L. Teng, “Numerical and simplified methods for the calculation of the total horizontal wave force on a perforated caisson with a top cover,”
*Coastal Engineering*, vol. 54, no. 1, pp. 67–75, 2007. - Meringolo, D.D. F. Aristodemo, P.
Veltri, “SPH numerical modeling of wave-perforated breakwater interaction”,
Coastal Engineering vol. 101 pgs. 48-68, 2015.
- Antuono, M., Colagrossi, A., Marrone, S., Molteni, D. Free-surface flows solved by means of SPH schemes with numerical diffusive terms.
*Computer Physics Communications*, 181:532–549, 2010. Molteni, D., Colagrossi, A. A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH.

*Computer Physics Communications*, 180:861–872, 2009.