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Finite Element Model for Laplace Equation
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Finite Element Model for Laplace Equation

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Abstract:

The mild-slope equation has widely been used for calculation of shallow water wave transformation. Recently, its extended version was introduced, which is capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. Here, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of the wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize it. The computational domain is discretized with proper finite elements, while the radiation condition at infinity is treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission. Analysis is also made for the case where a solid structure is floated near the still water level.

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Periodical:

Applied Mechanics and Materials (Volume 267)

Pages:

9-12

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.267.9

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Online since:

December 2012

Authors:

Sang Oh Shim, Tae Hwa Jung, Sang Chul Kim, Ki Chan Kim

Keywords:

Finite Element Method (FEM), Laplace Equation, Mild-Slope Equation

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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