A Mathematical Approach to Dampening Sea Waves Using Submerged Permeable Breakwater


  • J.L. Marpaung Magister of Mathematics, Universitas Sumatera Utara, Indonesia https://orcid.org/0000-0002-4645-6148
  • Tulus Mathematics Department Universitas Sumatera Utara
  • Parapat Gultom Mathematics Department Universitas Sumatera Utara




Breakwater, Finite Element Method, Modelling, Navier-Stokes Equation, Simulation


A wave is an energy that can propagate with a medium; the propagation of a wave moves with respect to time by carrying energy that moves with velocity per unit of time. Sea waves are one of the propagating wave problems that are broken down to produce wave propagation with a relatively inhomogeneous minimum amplitude and speed of sea waves, which have their own difficulties in solving them numerically. This study aims to analyze the stability of wave propagation on submerged breakwaters. This research will approximate the finite discretization of the breakwater domain and then combine it with the Finite Element Method to determine the moving elements of the velocity of fluid flow through a porous submerged breakwater.  The research has explained the equation of the inflated wave and the simulated representation displayed on the wave breakdown process, the point that becomes the center of the waves breakdown will give a focused red color indicator meaning there is a change in momentum and potential energy that occurs and then changes the colour of the post-flattering of the sea wave so that the sinking wave breaker is a method to obtain the minimum speed and amplitude values that can be used for coastal engineering.



GS Cited Analysis


Download data is not yet available.

Author Biographies

Tulus, Mathematics Department Universitas Sumatera Utara



Parapat Gultom, Mathematics Department Universitas Sumatera Utara




Abdul Ghani, F. A., Ramli, M. S., Md Noar, N. A. Z., Mohd Kasim, A. R., & Greenhow, M. (2017). Mathematical modelling of wave impact on floating breakwater. Journal of Physics: Conference Series, 890(1). https://doi.org/10.1088/1742-6596/890/1/012005

Bai, H., Chow, K. W., & Yuen, M. (2022). Exact solutions for the shallow water equations in two spatial dimensions: A model for finite amplitude rogue waves. Partial Differential Equations in Applied Mathematics, 5(December 2021). https://doi.org/10.1016/j.padiff.2022.100360

Bao, Q., Wang, M., Dai, G., Chen, X., Song, Z., & Li, S. (2022). rna Jou. Swarm and Evolutionary Computation, 106048, 101161. https://doi.org/10.1016/j.rinp.2022.106199

Fujima, K. (2006). Effect of a submerged bay-mouth breakwater on tsunami behavior analyzed by 2D/3D hybrid model simulation. Handbook of Environmental Chemistry, Volume 5: Water Pollution, 39(2), 179–193. https://doi.org/10.1007/s11069-006-0022-x

Han, M. M., & Wang, C. M. (2021). Modelling wide perforated breakwater with horizontal slits using Hybrid-BEM method. Ocean Engineering, 222(December 2020), 108630. https://doi.org/10.1016/j.oceaneng.2021.108630

Khater, M. M. A., & Botmart, T. (2022). Unidirectional shallow water wave model; Computational simulations. Results in Physics, 42(September), 106010. https://doi.org/10.1016/j.rinp.2022.106010

Kounadis, G., & Dougalis, V. A. (2020). Galerkin finite element methods for the Shallow Water equations over variable bottom. Journal of Computational and Applied Mathematics, 373(xxxx), 112315. https://doi.org/10.1016/j.cam.2019.06.031

Liu, T. P., & Yu, S. H. (2014). Boundary Wave Propagator for Compressible Navier–Stokes Equations. Foundations of Computational Mathematics, 14(6), 1287–1335. https://doi.org/10.1007/s10208-013-9180-x

Rupali, & Kumar, P. (2021). Mathematical modeling of arbitrary shaped harbor with permeable and impermeable breakwaters using hybrid finite element method. Ocean Engineering, 221(December 2020), 108551. https://doi.org/10.1016/j.oceaneng.2020.108551

Tulus, Khairani, C., Marpaung, T. J., & Suriati. (2019). Computational Analysis of Fluid Behaviour Around Airfoil with Navier-Stokes Equation. Journal of Physics: Conference Series, 1376(1). https://doi.org/10.1088/1742-6596/1376/1/012003

Tulus, Marpaung, J. L., Marpaung, T. J., & Suriati. (2020). Computational analysis of heat transfer in three types of motorcycle exhaust materials. Journal of Physics: Conference Series, 1542(1). https://doi.org/10.1088/1742-6596/1542/1/012034

Tulus, Marpaung, T. J., & Suriati. (2019). Computational Analysis of Water Wheel for Hydro-Electric Power. Journal of Physics: Conference Series, 1376(1). https://doi.org/10.1088/1742-6596/1376/1/012017

Winarta, B., Damarnegara, A., Anwar, N., & Juwono, P. (2018). Analysis of Waikelo Port Breakwater Failure through 2D Wave Model. Civil and Environmental Science, 001(02), 088–095. https://doi.org/10.21776/ub.civense.2018.00102.6

Yu, S., & Huang, L. (2022). Exact solutions of the generalized (2+1)-dimensional shallow water wave equation. Results in Physics, 42(September), 1–6. https://doi.org/10.1016/j.rinp.2022.106020


Crossmark Updates

How to Cite

Marpaung, J., Tulus, & Gultom, P. (2023). A Mathematical Approach to Dampening Sea Waves Using Submerged Permeable Breakwater. Sinkron : Jurnal Dan Penelitian Teknik Informatika, 8(3), 1278-1286. https://doi.org/10.33395/sinkron.v8i3.12489