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

Silalahi F.T.R.a, Budhi W.S.b, Adytia D.c, Van Groesen E.c

a Del Institute of Technology, Laguboti, Tobasa, Sumatera Utara, Indonesia
b Department of Mathematics, FMIPA ITB, Indonesia
c Department of Applied Mathematics, University of Twente, Netherlands
d Labmath Indonesia, Bandung, Indonesia

[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2015 AIP Publishing LLC.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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1063/1.4930628[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]