船舶辐射水动力数值预报的精细积分法及改进
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摘要
为减小由于大、小时间区域划分不明确导致的三维时域Green函数的数值误差,对小时间区域采用级数展开,对过渡区域及大时间区域采用精细积分法对三维时域Green函数进行精细地数值计算.基于三维时域Green函数求解船舶辐射力,分别对Wigley型船和S60型船进行数值计算.结果表明,水动力系数数值计算结果与试验结果及文献结果吻合较好,证明了所建模型的可靠性.
To reduce the numerical error of three-dimension time-domain Green's function due to unclear partition between small time computational domain and large time computation domain,the series expansion was adopted in small time computation domain,while the precise numerical calculation of three-dimensional time-domain Green's function was adopted in both transition domain and large time computation domain by using precise integration. Then,the radiation forces for a Wigley hull and a S60 hull were solved respectively based on three-dimensional time-domain Green's function.Results show that the hydrodynamic coefficients and wave exciting forces are in good agreements with both experimental results and published results,which verify the reliability of the proposed model.
To reduce the numerical error of three-dimension time-domain Green's function due to unclear partition between small time computational domain and large time computation domain,the series expansion was adopted in small time computation domain,while the precise numerical calculation of three-dimensional time-domain Green's function was adopted in both transition domain and large time computation domain by using precise integration. Then,the radiation forces for a Wigley hull and a S60 hull were solved respectively based on three-dimensional time-domain Green's function.Results show that the hydrodynamic coefficients and wave exciting forces are in good agreements with both experimental results and published results,which verify the reliability of the proposed model.
引文
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[2]KING B. W. Time domain analysis of wave exciting forces on ships and bodies:Report No. 306[R]. Ann Arbor,Michigan:University of Michigan,1987.
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[7]张腾,任俊生,李志富,等.时域格林函数的新实用数值计算方法[J].大连海事大学学报,2018,44(1):1-8.ZHANG T,REN J S,LI Z F,et al. A new and practical numerical calculation method for time-domain Green function[J]. Journal of Dalian Maritime University,2018,44(1):1-8.(in Chinese)
[8]JOURNE J M J. Experiments and calculations on four Wigley hull forms:Report 0909[R]. Delft:Delft University of Technology,1992.
[9]MAGEE A R,BECK R F. Compendium of ship motion calculations using linear time-domain analysis:Report No. 310[R]. Ann Arbor,Michigan:University of Michigan,1988.
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[11]申亮,朱仁传,缪国平,等.深水时域格林函数的实用数值计算[J].水动力学研究与进展,2007,22(3):380-386.SHEN L,ZHU R C,MIAO G P,et al. A practical numerical method for deep water time-domain Green function[J]. Journal of Hydrodynamics,2007,22(3):380-386.(in Chinese)
[2]KING B. W. Time domain analysis of wave exciting forces on ships and bodies:Report No. 306[R]. Ann Arbor,Michigan:University of Michigan,1987.
[3]CLEMENT A H. An ordinary differential equation for the Green function of time-domain free-surface hydrodynamics[J]. Journal of Engineering Mathematics,1998,33(2):201-217.
[4]CHUANG J M,QIU W,PENG H. On the evaluation of time-domain Green function[J]. Ocean Engineering,2007,34(7):962-969.
[5]LI Z F,REN H L,TONG X W,et al. A precise computation method of transient free surface Green function[J].Ocean Engineering,2015,105:318-326.
[6]ZHONG W X. On precise integration method[J]. Journal of Computational and Applied Mathematics,2004,163:59-78.
[7]张腾,任俊生,李志富,等.时域格林函数的新实用数值计算方法[J].大连海事大学学报,2018,44(1):1-8.ZHANG T,REN J S,LI Z F,et al. A new and practical numerical calculation method for time-domain Green function[J]. Journal of Dalian Maritime University,2018,44(1):1-8.(in Chinese)
[8]JOURNE J M J. Experiments and calculations on four Wigley hull forms:Report 0909[R]. Delft:Delft University of Technology,1992.
[9]MAGEE A R,BECK R F. Compendium of ship motion calculations using linear time-domain analysis:Report No. 310[R]. Ann Arbor,Michigan:University of Michigan,1988.
[10]HESS J L,SMITH A M O. Calculation of non-lifting potential flow about arbitrary three-dimensional bodies[J].Journal of Ship Research,1964,8(2):22-44.
[11]申亮,朱仁传,缪国平,等.深水时域格林函数的实用数值计算[J].水动力学研究与进展,2007,22(3):380-386.SHEN L,ZHU R C,MIAO G P,et al. A practical numerical method for deep water time-domain Green function[J]. Journal of Hydrodynamics,2007,22(3):380-386.(in Chinese)