# Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea

Fitriani Tupa R. Silalahi, Wono Setya Budhi, Didit Adytia, E. van Groesen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

### Abstract

One interesting phenomena is investigating the movement of ships at the sea. To start with the investigation in modelling of this problem, we will assume that the ship is only a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in parallel directions to the ship. Therefore, we simply use the two-dimensional Laplace equation in this problem. In the section that describes the surface of sea, Neumann boundary condition is imposed in part related to the ship and the Dirichlet boundary condition for others. Then on the other three boundaries, we imposed the Neumann boundary condition by assuming that the water does not flow on the bottom, and both end. The model is solved by numerical solution using the finite element method. Velocity potential solution on the whole domain is demonstrated as a result of the implementation of the finite element method. In this paper, we initiate an investigation with assuming that the ship is on the water so that the domain of the Laplace equation is rectangular. Then we assume the drift ship. Furthermore, we also study the dependence of width and depth of the domain to the velocity potential.

Original language English 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014 2–3 November 2014, Bandung, Indonesia Acep Purqon, Taufiq Hidayat, Reuben Jih-Ru Hwu American Institute of Physics 978-0-7354-1324-5 https://doi.org/10.1063/1.4930628 Published - 30 Sep 2015

### Publication series

Name AIP Conference Proceedings 1 1677 0094-243X 1551-7616

### Fingerprint

Laplace equation
ships
boundary conditions
finite element method
water flow
floating
water

### Cite this

Silalahi, F. T. R., Budhi, W. S., Adytia, D., & van Groesen, E. (2015). Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea. In A. Purqon, T. Hidayat, & R. J-R. Hwu (Eds.), 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia  (AIP Conference Proceedings; Vol. 1677, No. 1). American Institute of Physics. https://doi.org/10.1063/1.4930628
Silalahi, Fitriani Tupa R. ; Budhi, Wono Setya ; Adytia, Didit ; van Groesen, E. / Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea. 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia. editor / Acep Purqon ; Taufiq Hidayat ; Reuben Jih-Ru Hwu. American Institute of Physics, 2015. (AIP Conference Proceedings; 1).
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abstract = "One interesting phenomena is investigating the movement of ships at the sea. To start with the investigation in modelling of this problem, we will assume that the ship is only a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in parallel directions to the ship. Therefore, we simply use the two-dimensional Laplace equation in this problem. In the section that describes the surface of sea, Neumann boundary condition is imposed in part related to the ship and the Dirichlet boundary condition for others. Then on the other three boundaries, we imposed the Neumann boundary condition by assuming that the water does not flow on the bottom, and both end. The model is solved by numerical solution using the finite element method. Velocity potential solution on the whole domain is demonstrated as a result of the implementation of the finite element method. In this paper, we initiate an investigation with assuming that the ship is on the water so that the domain of the Laplace equation is rectangular. Then we assume the drift ship. Furthermore, we also study the dependence of width and depth of the domain to the velocity potential.",
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Silalahi, FTR, Budhi, WS, Adytia, D & van Groesen, E 2015, Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea. in A Purqon, T Hidayat & RJ-R Hwu (eds), 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia., 030006, AIP Conference Proceedings, no. 1, vol. 1677, American Institute of Physics. https://doi.org/10.1063/1.4930628

Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea. / Silalahi, Fitriani Tupa R.; Budhi, Wono Setya; Adytia, Didit; van Groesen, E.

5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia. ed. / Acep Purqon; Taufiq Hidayat; Reuben Jih-Ru Hwu. American Institute of Physics, 2015. 030006 (AIP Conference Proceedings; Vol. 1677, No. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Silalahi FTR, Budhi WS, Adytia D, van Groesen E. Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea. In Purqon A, Hidayat T, Hwu RJ-R, editors, 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia. American Institute of Physics. 2015. 030006. (AIP Conference Proceedings; 1). https://doi.org/10.1063/1.4930628