Effect of Interparticle Distance on Smoothed Particle Hydrodynamics on Wave Transformation Through Submerged Breakwater

Beach abrasion and erosion are problems that many beaches in Indonesia experience. Waves are the most influential processes in this phenomenon. When the waves move towards the coast, they will transform, generating currents near the coast. Currents moving along the coast displace sediment on the beach, causing changes in the shoreline. So it is necessary to carry out coastal protection efforts so that abrasion does not occur, which results in the erosion of coastal areas so that the island’s area is reduced and the coastline retreats. To overcome this problem, one of the supporting facilities is a submerged breakwater. In this paper, researchers will numerically study the effect of particle size on smoothed particle hydrodynamics (SPH) when waves pass through a submerged breakwater structure. The simulation is carried out on a Numerical Wave Tank (NWT), the piston is at the end of the tank, and the structure of the submerged breakwater is set according to the experimental scenario. The distance between the particles varied from 0.03, 0.025, 0.02, 0.015, and 0.01. The results show that the smaller the distance between the particles used, the wave elevation results are closer to the experimental model.


Introduction
Indonesia is an archipelagic country with a long coastline.As an area bordering the ocean, the coast also has the potential to experience damage, such as erosion, sedimentation, and damage to coastal areas which can cause changes in the existing coastline [1]- [7] and disrupt beach tourism [8] [9].These coastal problems can be overcome by natural protection with mangroves or bamboo [10]- [12] or by building protective structures to protect the coastline from existing problems.Coastal protection structures can be either floating or fixed breakwaters.
Floating breakwaters have been extensively studied both experimentally and numerically by researchers [13]- [24].This floating breakwater has advantages, including that it can be applied in seas with depths of more than 10 feet and soft seabed soil conditions [13] [14], causing minimal impact on water circulation, sediment transport, and fish migration [13], effective absorb waves of less than 2 meters [13], this structure can also be moved to another location with a different layout [13] [14] [16].However, this structure is less effective at damping short waves (wave period 6 s and frequency 1.6 rad/s).If the mooring system fails, it will cause an overall structural failure [21], and the cost of maintaining a floating breakwater is higher than that of a conventional breakwater [16].Coastal protection of fixed breakwater types can be in seawalls, seawalls, bulkheads, revetments, groins, and breakwaters [1].This structure can work effectively in shallow water.Breakwater is a structure that effectively reduces wave energy before it reaches the coast and protects the beach.Waves that hit the breakwater, some of their energy will be reflected, transmitted, and partially destroyed (dissipated).However, breakwaters can also hinder the beauty of a beach.The best solution is with a submerged breakwater structure.A submerged breakwater is a structure whose top is below or equal to sea level.So that breakwaters will not hinder tourists who enjoy the beauty of the beach.In addition, another advantage of submerged breakwaters is that the waves that pass through this structure do not experience a change in wave direction, resulting in no negative impact on the surrounding coast.Several submerged breakwaters have been applied in Indonesia, including Tanah Lot Bali, Peburan Bali Beach, Pasir Putih Karawang Beach, etc.
The transformation of waves passing through submerged structures is related to the movement of waves on the surface.This phenomenon can be investigated experimentally and numerically and is a challenge for experts working in the coastal sector.This study used a numerical approach with the smoothed particle hydrodynamics (SPH) method, which is very good at producing wave simulations.Moreover, SPH can be visualized to get a clear simulation picture.Research on the application of the SPH model has been widely studied by researchers [12] [25]- [28].This research was carried out in a numerical wave tank (NWT) with a piston at the end of the tank and a structure in the form of a submerged breakwater.The effect of particle size will be tested for its accuracy and ability to transmit waves using the SPH method when it passes through a submerged breakwater.

Methods
Smoothed Particle Hydrodynamics (SPH) is a non-mesh Lagrangian method often used for applications in Computational Fluid Dynamics (CFD) where particles represent flow, interact with structures, and can exhibit large deformations with moving boundaries [29].The constituent equations of this model (equations 1-4) consist of the momentum equation, Lagrange, states, continuity in the delta-SPH form, which functions to reduce fluctuations, and the momentum equation with a fluid particle approach.
Experimental data that has been done before [30] is used for the simulation of the SPH model.The wave parameters used in the numerical model also refer to the time the experiment was carried out; namely, the wave height and period were 0.1 m and 1.47 s, with the water depth set to 0.6 m.

Analysis and Discussion
SPH numerical modeling was carried out by analyzing five different distances between particles.The most optimum distance between particles will be obtained for this study.The distance between the particles used is as follows: 0.03 m, 0.025 m, 0.02 m, 0.015 m, and 0.01 m.Validation is comparing the results of numerical modeling with experimental data.In the study referring to the experiment [30], model validation occurred when the wave transformation passed through the submerged breakwater.Changes in water level elevation are recorded on wave probes 1-6, as shown in Fig. 1 above.The results of the running program at five variations of the distance between particles can be seen by visualizing the results in the Paraview software (Fig. 2).The model results show that the smaller the distance between the particles, the better and conversely, the larger the distance, the less noticeable the particles are.This condition will certainly affect the accuracy of the simulation results.
The weakness of the distance between particles that produces better and clearer images is that the running time becomes longer.Nevertheless, this also depends on the specifications of the PC used.This DualSPHysics software is intended to use the GPU (Graphics Processing Unit) but can still use the CPU (Central Processing Unit).The difference between the CPU and GPU on DualSPhysics is the running time.This software is intended for utility use of the GPU.Therefore, if it is run with the GPU, it can be faster than using the CPU.The better the CPU or GPU specifications, the faster it can run.This research was conducted on a PC with the exact specifications for a simulation time of 120 seconds with a distance between particles of 0.03m, 0.025, 0.02, 0.015, and 0.01, requiring a running time of 4-6 hours, 10-14 hours, 19-26 hours, 38 -54 hours, and 72-94 hours, respectively (Table 1).It can be seen that the time difference is quite significant.Therefore, the running time is included in the criteria for selecting the distance between particles to obtain maximum results, the simulation time is efficient, and the error rate is low between the numerical and experimental results.
After running the DualSPHysics software, the results of the water level elevation in the form of a wave time series will be the output of this study.These results will be compared with the experimental results on the breakwater model and the input wave parameters.The smaller the deviation of the running numerical results from the experimental results, the better.The mean absolute percentage error (MAPE) method is used [31] to calculate the deviations.This method measures the accuracy of a forecast model made from the actual model.The smaller the value, the smaller the deviation of the forecast model from the actual model or, in other words, the closer the forecast model is to the actual model.
After running on DualSPHysics, use one of the post-processing tools on DualSPHysics to get wave elevation data that occurs at specific predetermined points according to experimental data, namely "MeasureTool".This tool adjusts the location for recording wave elevation data to the wave probe point in the experiment (Fig. 1).Based on Table 1, the running time and the deviation between numerical and experimental means that at a distance between particles of 0.01 m, the average error is at least 2.95%, but the time needed to complete the process is 72-94 hours.At a distance between particles of 0.015m, the error result is not too far from 0.01m; it requires a running time of 38-54, which is about 1.5 times faster than 0.01m.For distances of 0.03 m, 0.025 m, and 0.02 m, the resulting error results are no better 1298 (2024) 012001 IOP Publishing doi:10.1088/1755-1315/1298/1/0120014 than those of 0.01 m and 0.015 m, even though the time required for running is faster among the five distances between particles.Therefore in this study, the distance between particles of 0.015 m is the most efficient, considering that the resulting error is not too far at 0.01 m, and the time needed is more efficient and faster than 0.01m.

Conclusion
This study concluded that the SPH method could simulate wave transformations well, as evidenced by the relatively minor deviations in the water level elevation fluctuations from the model and experiment results.The smaller the distance between the particles, the smaller the deviation that occurs; in this study, 0.01 m is the best.However, 0.01 m requires the longest running time.Therefore for optimal results with more efficient time, 0.015 m is the best choice.

Figure 2 .
Figure 2. Visualization in Paraview software results from running models with various distance variations between particles.

Figure 3 .
Figure 3. Simulation of the SPH model of water level fluctuations when passing through a submerged breakwater at various distances between particles for each wave probe

Table 1 .
Error calculation between numerical and experimental model data