Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code

Mostafa Amini-Afshar, Harry B. Bingham

Research output: Contribution to conferencePaperResearchpeer-review

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Abstract

At the 32nd IWWWFB in Dalian, we presented our implementation of the far-field method for second-order wave drift forces based on the Kochin function, using the open-source seakeeping codeOceanWave3D-Seakeeping. In that work we used Maruo's method (Maruo, 1960), and calculated the added resistance by a line integral along the azimuthal angle XX around the body in the far-field. Some difficulties were encountered with regard to evaluating the singular and improper integrals, together with identifying the highest frequency limit where we can practically and reliably calculate the Kochin function by a numerical integration over the surface of the body. Motivated by discussions with Prof. Kashiwagi during this workshop (Kashiwagi, 2017), we subsequently applied the Hanaoka transformation (Maruo, 1960) to change the integration domain from Θ to a wave-number like variable m. This allows a method developed by Prof. Kashiwagi to be used to evaluate the relevant singular integrals, leading to more robust and accurate results. In this abstract, we outline the numerical method and present new calculations for the added resistance of a submerged and a floating spheroid, These results are compared with near-field solutions, and calculations using boundary element codes where applicable.
Original languageEnglish
Publication date2018
Number of pages4
Publication statusPublished - 2018
Event33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018) - Guidel-Plages, France
Duration: 4 Apr 20187 Apr 2018

Conference

Conference33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018)
CountryFrance
CityGuidel-Plages
Period04/04/201807/04/2018

Cite this

Amini-Afshar, M., & Bingham, H. B. (2018). Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code. Paper presented at 33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018), Guidel-Plages, France.
Amini-Afshar, Mostafa ; Bingham, Harry B. / Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code. Paper presented at 33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018), Guidel-Plages, France.4 p.
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Amini-Afshar, M & Bingham, HB 2018, 'Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code' Paper presented at 33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018), Guidel-Plages, France, 04/04/2018 - 07/04/2018, .

Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code. / Amini-Afshar, Mostafa; Bingham, Harry B.

2018. Paper presented at 33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018), Guidel-Plages, France.

Research output: Contribution to conferencePaperResearchpeer-review

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T1 - Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code

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N2 - At the 32nd IWWWFB in Dalian, we presented our implementation of the far-field method for second-order wave drift forces based on the Kochin function, using the open-source seakeeping codeOceanWave3D-Seakeeping. In that work we used Maruo's method (Maruo, 1960), and calculated the added resistance by a line integral along the azimuthal angle XX around the body in the far-field. Some difficulties were encountered with regard to evaluating the singular and improper integrals, together with identifying the highest frequency limit where we can practically and reliably calculate the Kochin function by a numerical integration over the surface of the body. Motivated by discussions with Prof. Kashiwagi during this workshop (Kashiwagi, 2017), we subsequently applied the Hanaoka transformation (Maruo, 1960) to change the integration domain from Θ to a wave-number like variable m. This allows a method developed by Prof. Kashiwagi to be used to evaluate the relevant singular integrals, leading to more robust and accurate results. In this abstract, we outline the numerical method and present new calculations for the added resistance of a submerged and a floating spheroid, These results are compared with near-field solutions, and calculations using boundary element codes where applicable.

AB - At the 32nd IWWWFB in Dalian, we presented our implementation of the far-field method for second-order wave drift forces based on the Kochin function, using the open-source seakeeping codeOceanWave3D-Seakeeping. In that work we used Maruo's method (Maruo, 1960), and calculated the added resistance by a line integral along the azimuthal angle XX around the body in the far-field. Some difficulties were encountered with regard to evaluating the singular and improper integrals, together with identifying the highest frequency limit where we can practically and reliably calculate the Kochin function by a numerical integration over the surface of the body. Motivated by discussions with Prof. Kashiwagi during this workshop (Kashiwagi, 2017), we subsequently applied the Hanaoka transformation (Maruo, 1960) to change the integration domain from Θ to a wave-number like variable m. This allows a method developed by Prof. Kashiwagi to be used to evaluate the relevant singular integrals, leading to more robust and accurate results. In this abstract, we outline the numerical method and present new calculations for the added resistance of a submerged and a floating spheroid, These results are compared with near-field solutions, and calculations using boundary element codes where applicable.

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Amini-Afshar M, Bingham HB. Accurate evaluation of the Kochin function for added resistance using a high-order finite difference-based seakeeping code. 2018. Paper presented at 33rd International Workshop on Water Waves and Floating Bodies (IWWWFB 2018), Guidel-Plages, France.