### Abstract

The mild-slope equation has been used for calculation of the surface gravity water wave transformation. Recently, its extended versions were 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 new 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 get a finite element solution. The computational domain is discretized with an infinite element. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission.

Original language | English |
---|---|

Pages (from-to) | 4869-4874 |

Number of pages | 6 |

Journal | Information (Japan) |

Volume | 18 |

Issue number | 12 |

Publication status | Published - 2015 Dec 1 |

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### Keywords

- Finite element method
- Infinite element
- Laplace equation
- Mild-slope equation

### ASJC Scopus subject areas

- Information Systems

### Cite this

*Information (Japan)*,

*18*(12), 4869-4874.

**Finite element wave model for Laplace equation.** / Jung, Taehwa; Son, Sang Young.

Research output: Contribution to journal › Article

*Information (Japan)*, vol. 18, no. 12, pp. 4869-4874.

}

TY - JOUR

T1 - Finite element wave model for Laplace equation

AU - Jung, Taehwa

AU - Son, Sang Young

PY - 2015/12/1

Y1 - 2015/12/1

N2 - The mild-slope equation has been used for calculation of the surface gravity water wave transformation. Recently, its extended versions were 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 new 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 get a finite element solution. The computational domain is discretized with an infinite element. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission.

AB - The mild-slope equation has been used for calculation of the surface gravity water wave transformation. Recently, its extended versions were 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 new 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 get a finite element solution. The computational domain is discretized with an infinite element. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission.

KW - Finite element method

KW - Infinite element

KW - Laplace equation

KW - Mild-slope equation

UR - http://www.scopus.com/inward/record.url?scp=84959154223&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959154223&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84959154223

VL - 18

SP - 4869

EP - 4874

JO - Information (Japan)

JF - Information (Japan)

SN - 1343-4500

IS - 12

ER -