Simulation of a Wave Hydrodynamic Numerical Model on a Single Vertical Porous Breakwater

One of the problems in the coastal area is a change in the coastline in the form of a coastline retreat which results in the loss or damage of infrastructure and settlement facilities caused by extreme sea wave activity. One way to anticipate this problem is to build a breakwater. This research is focused on the effect of porosity and freeboard on the transmission and reflection of waves in a single vertical porous breakwater. Numerical modeling was done using a 3D Numerical Wave Tank (NWT) based on Smoothed Particle Hydrodynamic (SPH). The numerical model results show that the average transmission and reflection coefficients are 0.58 and 0.42. In addition, it can be seen that the freeboard and porosity influence the value of the transmission and reflection coefficients. Generally, the smaller the freeboard, the greater the transmission coefficient and the smaller the reflection coefficient. Meanwhile, the greater the porosity, the greater the transmission coefficient, and vice versa, the smaller the reflection.


Introduction
As an archipelagic country, Indonesia has coastal areas with great potential to support human survival, so their existence is used intensively.The potential of human and coastal natural resources in Indonesia is an outstanding potential and a challenge that can be utilized as well as possible.One of these uses is the construction of a port.However, if the port construction is not carried out properly, it will impact the surrounding beaches, namely sedimentation and erosion [1][2][3][4][5][6][7][8].Another problem about the coastal area is a change in the coastline in the form of a retreating coastline resulting in loss or damage to infrastructure facilities and settlements caused by high sea wave activity.
The solution to this problem can be done naturally, namely dampening the waves with mangrove plants [9][10][11][12][13] and bamboo [14] or adjusting the coastal border by implementing integrated coastal zone management (ICZM).Another way is to construct a coastal protection structure, such as a floating breakwater [15][16][17][18][19][20][21][22][23][24][25][26] or a fixed breakwater [27][28][29][30][31][32].This type of fixed breakwater, horizontal and vertical, is a very effective structure in protecting the coast by dissipating wave energy before it reaches the beach.In waves that hit the wave damper building, some of the energy will be reflected, transmitted, and partly destroyed (dissipated) through the breaking of the wave, which depends on the characteristics of the incident wave.Transmission (Ht) and reflection (Hr) waves are measured by the transmission coefficient (Kt) and reflection (Kr) parameters.Several previous studies have proven that the value of the transmission and reflection coefficients is strongly influenced by the height and period of the waves.
Increasing the length and height of the waves decreases the transmission coefficient, while the reflection coefficient is directly proportional to the length and height of the waves.
This study will focus on the vertical structure of porous breakwaters.The pore-shaped structure has the advantage that it can dampen wave energy by holding its energy through the pore so that the wave energy received by the structure is reduced.Apart from that, this pore-shaped structure is designed to utilize small stones to be included in the porous box frame because, at the time of construction, not every project site had natural stone available with the weight according to the design.Many researchers have carried out numerical modeling using Smoothed Particle Hydrodynamics (SPH) DualSPHysics 5.0 software before [33][34][35][36][37][38].This paper will apply an SPH-based analysis to obtain the transmission and reflection coefficients on a vertical porous breakwater.

Data and 3D models
The determination of the research variable is used to see its effect on what is being observed.In this study, numerical analysis will be carried out using the DualSPHysics software.After a literature study on previous studies, the impact of wave parameters on the structure will be reviewed further.Test data in this study used wave height and period, 0.1-0.18m and 1.35 and 1.8 seconds, respectively.
In this study, the 3D models that will be made include flume tanks, vertical porous breakwater structures, and beds.The 3D model creation was designed using the open-source software FreeCAD 0.20 (Fig. 1) because DualSPHysics does not have its interface yet.FreeCAD 0.20 software can add user interfaces from other software via "macros" from DualSPhysics 5.0.The specification data for the 3D Numerical Wave Tank (NWT) to be used has dimensions of 30.0m in length, 0.5m in width, and 1.0m in height (Fig. 2).By using the DualSPHysics 5.0 user interface, FreeCAD 0.20 can be used to adjust the piston motion on the flume tank model to generate waves.

Model Validation
The validation process in this study is used to determine the dimensions of the numerical wave tank (NWT) before finally proceeding with the model simulation process.This validation ensures that the model dimensions of the numerical flume tank used follow the physical and theoretical conditions and are feasible for use in the research being conducted.In this study, validation was carried out by comparing the numerical results using DualSPHysics with the experimental results of the physical model [39].The wave probe is placed according to the location determined in the physical model test.Wave probe 1 is placed 5 meters from the piston, which is used as wave input.Then wave probe 3 is placed 2 m away from the outermost structure, wave probe 2 is placed 3.5 m before wave probe 3, and wave probe 4 is 2 m behind the structure.
This numerical modeling was validated using sensitivity analysis using variations in the distance between different particles.This fact is done to get the optimum distance between particles in this research.The distance between the particles used is 0.03m, 0.02m and 0.01m.The results of the comparison of numerical model simulations and experiments are shown in Fig. 3 -5.Based on numerical modeling, it can be seen that the distance between particles affects the accuracy of the model results.The smaller the distance between the particles, the better the result.A distance between particles of 0.01 m has the lowest error rate between the distance between particles of 0.02 m and 0.03 m (Table ).However, the program simulation time on a computer with the same specifications will be longer.Good validation results show that the wave elevation between the numerical and physical models is not much different (Table 1).The error approach uses the mean absolute percentage error (MAPE) method [41].Table 1.MAPE calculation results for numerical and physical models

Results and Discussion
Analysis of the transmission coefficient Kt and Kr reflection was carried out based on the parameters of wave steepness and freeboard dimensions.The steepness of the waves shows a nondimensional variable due to the height and period of the waves expressed in H/gT 2 .The freeboard is a nondimensional variable due to the effect of freeboard height and waves (Rc/H), where these two variables are variables that affect the transmission coefficient (K t ) and reflection (K r ).In this numerical model simulation, the freeboard is varied with a height of 0.0m and 0.10m relative to sea level elevation (SWL).Porosity in the model is set by filling a porous concrete box with gravel of a specific size, and then the volume filled with gravel is compared to the volume of the entire porous box.This study set the porosity at 5% and 10%.
Based on the numerical model simulation results, it was found that the porosity vertical breakwaters were 0%, 5%, and 10% on the same freeboard (Fig. 6), indicating that Kt in a 5% porous vertical breakwater has a greater Kt value than without pores ( 0%).At 10% porosity, the value of Kt will be even greater because, in this condition, much wave energy is not entirely damped compared to without porosity.As for the influence of the steepness of the wave, it can be observed that the greater the steepness of the wave, the value of the transmission coefficient Kt also increases (Fig. 7).Conversely, the higher the freeboard (Rc = 0.1m), the lower the Kt value because the wave energy will be damped by the freeboard which is 0.1m above the SWL.The same thing also happens to the phenomenon of wave reflection.On a high freeboard (Rc=0.1m), the waves will be partially reflected to a greater extent than a structure with a freeboard in SWL (Rc=0.0m)(Fig. 8 and 9).

Conclusion
Based on the results of the numerical model simulation that has been done, it can be concluded that the greatest transmission coefficient is located at Rc = 0 and n = 10%, and the largest reflection coefficient is located at Rc = 0.1m and n = 5%, with an average of Kt and Kr of 0.58 and 0.42.Freeboard is very influential on Kt and Kr.The smaller the freeboard and the greater the porosity, the greater Kt.Conversely, Kr is greater if the freeboard is also larger.This fact proves that freeboard and Kt are inversely related.While porosity with Kt is directly proportional and Kr is inversely proportional.

Figure 3 .
Figure 3. Results of the validation of numerical and experimental models with a distance between particles of 0.03m

Figure 4 .Figure 5 . 7 Figure 6 .Figure 7 .Figure 8 . 8 Figure 9 .
Figure 4. Results of the validation of numerical and experimental models with a distance between particles of 0.02m