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Numerical investigation on second-order wave force and moment of ships with forward speed by frequency-domain higher-order coupled method based translating-pulsating panel and Rankine sources
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Yun-tao YANG1, 2, Jun-hua ZHAN3, Hui WANG4
Journal of Ship Mechanics | 2026, 30(9) : 1411 - 1423
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Journal of Ship Mechanics | 2026, 30(9): 1411-1423
• Hydrodynamics •
Numerical investigation on second-order wave force and moment of ships with forward speed by frequency-domain higher-order coupled method based translating-pulsating panel and Rankine sources
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Yun-tao YANG1, 2, Jun-hua ZHAN3, Hui WANG4
Affiliations
  • 1School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhenjiang 215600, China
  • 2Industrial Technology Research Institute (Advanced Metal Materials) of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang 215600, China
  • 3National Key Laboratory of Science and Technology on Hydrodynamics, China Ship Scientific Research Center, Wuxi 214082, China
  • 4Wuhan Second Ship Design and Research Institute, Wuhan 430205, China
Published: 2026-09-15 doi: 10.3969/j.issn.1007-7294.2026.09.002
Outline
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In order to predict the second-order force and moment of ships sailing in waves, the fluid domain is decomposed into two parts (where the steady flow effects are considered in the internal one), and a multi-domain coupled hydrodynamic model is established based on the continuity of the flow field. Then a higher-order coupled method is developed, in which nine-node quadratic elements are employed to discretize the boundary, Rankine source is adopted to deal with the complex boundary condition near the ship and higher-order translating-pulsating panel source Green’s function (i.e., analytical integral of the Green’s function over the higher-order panel) is derived over the control surface. On this basis, formulas for second-order force and moment in oblique waves are established under the weak scattering assumption. A numerical program is developed to calculate and analyze the second-order wave forces in surge/sway and yaw moment of various ships advancing in different wave directions. The results show that the present method is more stable and accurate than the traditional higher-order translating-pulsating source method based on Gaussian quadrature formula, as well as the lower-order constant panel method. It is generally applicable to different ship types sailing in both head and oblique waves.

second-order force and moment  /  higher-order translating-pulsating panel source  /  coupled method  /  nine-node quadratic element
杨云涛, 湛俊华, 王慧. 基于频域高阶移动脉动面源−Rankine耦合法的有航速船舶二阶波浪力（矩）数值预报研究. 船舶力学, 2026 , 30 (9) : 1411 -1423 . DOI: 10.3969/j.issn.1007-7294.2026.09.002
Yun-tao YANG, Jun-hua ZHAN, Hui WANG. Numerical investigation on second-order wave force and moment of ships with forward speed by frequency-domain higher-order coupled method based translating-pulsating panel and Rankine sources[J]. Journal of Ship Mechanics, 2026 , 30 (9) : 1411 -1423 . DOI: 10.3969/j.issn.1007-7294.2026.09.002
Appendix
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Year 2026 volume 30 Issue 9
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Article Info
doi: 10.3969/j.issn.1007-7294.2026.09.002
  • Receive Date：2026-02-06
  • Online Date：2026-11-03
  • Published：2026-09-15
Article Data
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History
  • Received：2026-02-06
Funding
Affiliations
    1School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhenjiang 215600, China
    2Industrial Technology Research Institute (Advanced Metal Materials) of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang 215600, China
    3National Key Laboratory of Science and Technology on Hydrodynamics, China Ship Scientific Research Center, Wuxi 214082, China
    4Wuhan Second Ship Design and Research Institute, Wuhan 430205, China
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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