### 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 |
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Title of host publication | 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014 |

Subtitle of host publication | 2–3 November 2014, Bandung, Indonesia |

Editors | Acep Purqon, Taufiq Hidayat, Reuben Jih-Ru Hwu |

Publisher | American Institute of Physics |

ISBN (Electronic) | 978-0-7354-1324-5 |

DOIs | |

Publication status | Published - 30 Sep 2015 |

### Publication series

Name | AIP Conference Proceedings |
---|---|

Number | 1 |

Volume | 1677 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Fingerprint

### Cite this

*5th International Conference on Mathematics and Natural Sciences, ICMNS 2014: 2–3 November 2014, Bandung, Indonesia*[030006] (AIP Conference Proceedings; Vol. 1677, No. 1). American Institute of Physics. https://doi.org/10.1063/1.4930628

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea

AU - Silalahi, Fitriani Tupa R.

AU - Budhi, Wono Setya

AU - Adytia, Didit

AU - van Groesen, E.

PY - 2015/9/30

Y1 - 2015/9/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84984532153&partnerID=8YFLogxK

U2 - 10.1063/1.4930628

DO - 10.1063/1.4930628

M3 - Conference contribution

AN - SCOPUS:84984532153

T3 - AIP Conference Proceedings

BT - 5th International Conference on Mathematics and Natural Sciences, ICMNS 2014

A2 - Purqon, Acep

A2 - Hidayat, Taufiq

A2 - Hwu, Reuben Jih-Ru

PB - American Institute of Physics

ER -