FEM model of the modified mild slope equation

Ni Yunlin; Teng Bin; Cong Longfei

doi:10.3969/j.issn.0253-4193.2017.01.011

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Ni Yunlin, Teng Bin, Cong Longfei. FEM model of the modified mild slope equation[J]. Haiyang Xuebao, 2017, 39(1): 104-110. doi: 10.3969/j.issn.0253-4193.2017.01.011

Citation:

Ni Yunlin, Teng Bin, Cong Longfei. FEM model of the modified mild slope equation[J]. Haiyang Xuebao, 2017, 39(1): 104-110. doi: 10.3969/j.issn.0253-4193.2017.01.011

Ni Yunlin, Teng Bin, Cong Longfei. FEM model of the modified mild slope equation[J]. Haiyang Xuebao, 2017, 39(1): 104-110. doi: 10.3969/j.issn.0253-4193.2017.01.011

Citation:

Ni Yunlin, Teng Bin, Cong Longfei. FEM model of the modified mild slope equation[J]. Haiyang Xuebao, 2017, 39(1): 104-110. doi: 10.3969/j.issn.0253-4193.2017.01.011

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FEM model of the modified mild slope equation

doi: 10.3969/j.issn.0253-4193.2017.01.011

1.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;School of Port and Transportation Engineering, Zhejiang Ocean University, Zhoushan 316022, China
2.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

Received Date: 2016-03-07
Rev Recd Date: 2016-05-17

Abstract

Abstract

Compared with the mild slope equation, the bottom curvature and slope-squared terms are contained in the modified mild slope equation, which increases the complexity of solving the equation numerically. In this paper, the physical domain is divided into a finite inner region and an infinite outer region. The inner region of a variable depth is studied with the modified mild slope equation, and the outer region has a constant water depth, the velocity potential satisfying the Helmholtz equation. The bottom curvature and slope-squared terms in the equation are evaluated from the input bathymetry at each node of every element using the interpolation functions. With the boundary matching method and Gaussian elimination technique, the finite element equations are established and solved. Then, wave transformation over a Homma Island and a circular shoal is simulated respectively, and the results agree well with analytical solutions and experimental data, verifying the validity of the FEM model in this paper. Meanwhile, the comparison between the numerical and experimental results indicates the modified mild slope equation can provide more accurate predictions than the mild slope equation for wave propagation over relatively steep bathymetry.
- the modified mild slope equation,
- finite element method,
- Homma Island,
- circular shoal

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References(15)

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