A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advanc...A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advancing in waves.In this method,the 9-node bi-quadratic curvilinear elements employed to discretize the mixed-source/dipole boundary integral equation are mapped into the parametric plane through a coordinate transformation.Then in order to ease the numerical instability problem,a novel analytical quadrature is derived to calculate the influence coefficients by changing the integral order and using integration by parts.The singularity caused by infinite discontinuity is analyzed and eliminated by adopting some mathematical techniques.Through the calculations of panel integrals of Green’s function and its x-derivative,the analytical integral method is proved to be always accurate even for field points approaching the free surface,where numerical quadrature is impossible to give reasonable results.Based on this,a higher-order seakeeping program is developed and applied in the motion response prediction of two different types of ships(i.e.,a wall-sided ship Wigley III and a non-wall-sided ship S175).By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating and higher-order Green’s function methods based on traditional Gauss quadrature,it is found that the HOBEM based on analytical quadrature is of better accuracy and stability.For the non-wall-sided ship,only the present method can produce reasonable pre-diction of motion responses,while obvious oscillatory phenomenon is observed in the results of the other two numerical methods based on Gauss quadrature.展开更多
A practical numerical tool is developed to evaluate ship waves of high speed displacement ships on the basis of potential flow theory, in which high order boundary element method (HOBEM) based on biquadratic shape fun...A practical numerical tool is developed to evaluate ship waves of high speed displacement ships on the basis of potential flow theory, in which high order boundary element method (HOBEM) based on biquadratic shape functions is applied to solve the boundary value problem. Since the sinkage and trim of ship at high speeds are notable, influences of ship attitude on wave drag are investigated and three kinds of models are used to evaluate them. To make the numerical approach highly efficient, an incomplete LU factorization preconditioner is adopted and incorporated with the restarted generalized minimal residual method GMRES (m) to solve the boundary integral equation. A corresponding Fortran code is developed and applied to evaluate ship waves of the Wigley hull and 4a model, a transom stem ship. Computations are performed for both monohulls and catamarans over a wide range of Froude numbers (Fr= 0.10-l.00). Numerical issues including mesh convergence and computational efficiency are investigated at first. Computed results of the wave drag, sinkage and trim show generally good agreement with experimental data. Reasonable wave patterns are obtained and physical phenomena that wake angle max, where the largest waves occur, would become narrow at high speeds is also captured by the present computations. Numerical results indicate the proposed method would be accurate and efficient to evaluate resistance for hull design of high speed displacement ship.展开更多
A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity poten...A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.展开更多
The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element ...The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method （HOBEM）. In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.展开更多
To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element m...To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.展开更多
To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform （pFFT） method has been proposed for infinite depth problems with the deep water Green function, as i...To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform （pFFT） method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Tocplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.展开更多
To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed...To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.展开更多
Fully nonlinear water entry of a cone into waves with gravity effect has been analyzed based on a three-dimensional(3D)higher-order boundary method(HOBEM).The total velocity potential at the initial time is divided in...Fully nonlinear water entry of a cone into waves with gravity effect has been analyzed based on a three-dimensional(3D)higher-order boundary method(HOBEM).The total velocity potential at the initial time is divided into the incident and scattering components.In the subsequent time steps,the solution of the velocity potential is defined as a whole through instantaneous boundary conditions.Based on the image theory,a modified Green function is applied to establish the integral equations so that only half of the calculation domain is considered and the seabed can be excluded.The free surface elevation is tracked along a given azimuth plane in the polar coordinate system,while the horizontal motion of the water particle is updated by using a segment-spring analogy method,which redistributes nodes and maintains mesh connectivity according to linear stiffness.An auxiliary function is applied to solve the pressure distribution,instead of directly calculating time derivative of the velocity potential.The high accuracy of the present numerical method is achieved through a detailed convergence study and comparison with results in the literature.Simulations are emphatically performed to examine the effects of gravity,wave nonlinearity,entry location,and oblique entry.展开更多
基金financially supported by the National Natural Science Foundation of China (Grant No. 52101357)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 21KJB580012)the Scientific Research Start-up Fund of Jiangsu University of Science and Technology
文摘A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advancing in waves.In this method,the 9-node bi-quadratic curvilinear elements employed to discretize the mixed-source/dipole boundary integral equation are mapped into the parametric plane through a coordinate transformation.Then in order to ease the numerical instability problem,a novel analytical quadrature is derived to calculate the influence coefficients by changing the integral order and using integration by parts.The singularity caused by infinite discontinuity is analyzed and eliminated by adopting some mathematical techniques.Through the calculations of panel integrals of Green’s function and its x-derivative,the analytical integral method is proved to be always accurate even for field points approaching the free surface,where numerical quadrature is impossible to give reasonable results.Based on this,a higher-order seakeeping program is developed and applied in the motion response prediction of two different types of ships(i.e.,a wall-sided ship Wigley III and a non-wall-sided ship S175).By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating and higher-order Green’s function methods based on traditional Gauss quadrature,it is found that the HOBEM based on analytical quadrature is of better accuracy and stability.For the non-wall-sided ship,only the present method can produce reasonable pre-diction of motion responses,while obvious oscillatory phenomenon is observed in the results of the other two numerical methods based on Gauss quadrature.
基金National Natural Science Foundation of China(Grant Nos.51479117,51579147)the National Key Basic Research Development Program of China(973 Program,Grant No.2014CB046203).
文摘A practical numerical tool is developed to evaluate ship waves of high speed displacement ships on the basis of potential flow theory, in which high order boundary element method (HOBEM) based on biquadratic shape functions is applied to solve the boundary value problem. Since the sinkage and trim of ship at high speeds are notable, influences of ship attitude on wave drag are investigated and three kinds of models are used to evaluate them. To make the numerical approach highly efficient, an incomplete LU factorization preconditioner is adopted and incorporated with the restarted generalized minimal residual method GMRES (m) to solve the boundary integral equation. A corresponding Fortran code is developed and applied to evaluate ship waves of the Wigley hull and 4a model, a transom stem ship. Computations are performed for both monohulls and catamarans over a wide range of Froude numbers (Fr= 0.10-l.00). Numerical issues including mesh convergence and computational efficiency are investigated at first. Computed results of the wave drag, sinkage and trim show generally good agreement with experimental data. Reasonable wave patterns are obtained and physical phenomena that wake angle max, where the largest waves occur, would become narrow at high speeds is also captured by the present computations. Numerical results indicate the proposed method would be accurate and efficient to evaluate resistance for hull design of high speed displacement ship.
基金financially supported by the National Natural Science Foundation of China (Grant Nos.52271276,52271319,and 52201364)the Natural Science Foundation of Jiangsu Province (Grant No.BK20201006)。
文摘A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.
基金supported by the National Natural Science Foundation of China(51222902,51221961,and 51379032)the Program for New Century Excellent Talents in University(NCET-130076)+2 种基金The Fundamental Research Fund for the Central University(HEUCF140103)The Open Fund of State Key Laboratory of Coastal and Offshore Engineering(LP1407)the Lloyd’s Register Foundation (LRF) through the Joint Centre Involving University College London,Shanghai Jiaotong University and Harbin Engineering University
文摘The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method （HOBEM）. In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.
基金supported by the National Natural Science Foundation of China(Grant Nos.51179028,51222902,and 51221961)the National Basic Research Program of China(973 Program,Grant No.2011CB013703)+1 种基金the Program for New Century Excellent Talents in University(Grant No.NCET-13-0076)the Fundamental Research Funds for the Central Universities(Grant No.DUT13YQ104)
文摘To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.
基金supported by the National Natural Science Foundation of China(Grant Nos.51490672 and 51379032)
文摘To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform （pFFT） method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Tocplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.
基金Supported by the National Natural Science Foundation of China under (Grant No.107 72040,50709005 and 50921001)the Major National Science and Technology Projects of China under (Grant No.2008ZX05026-02)the Open Fund of State Key Laboratory of Ocean Engineering
文摘To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52025112,51861130358,and 51609109)the State Key Laboratory of Ocean Engineering,China(Shanghai Jiao Tong University)(Grant No.1905)+1 种基金the Newton Advanced Fellowships(Grant No.NAF\R1\180304)by the Royal Societythe Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX20_3156).
文摘Fully nonlinear water entry of a cone into waves with gravity effect has been analyzed based on a three-dimensional(3D)higher-order boundary method(HOBEM).The total velocity potential at the initial time is divided into the incident and scattering components.In the subsequent time steps,the solution of the velocity potential is defined as a whole through instantaneous boundary conditions.Based on the image theory,a modified Green function is applied to establish the integral equations so that only half of the calculation domain is considered and the seabed can be excluded.The free surface elevation is tracked along a given azimuth plane in the polar coordinate system,while the horizontal motion of the water particle is updated by using a segment-spring analogy method,which redistributes nodes and maintains mesh connectivity according to linear stiffness.An auxiliary function is applied to solve the pressure distribution,instead of directly calculating time derivative of the velocity potential.The high accuracy of the present numerical method is achieved through a detailed convergence study and comparison with results in the literature.Simulations are emphatically performed to examine the effects of gravity,wave nonlinearity,entry location,and oblique entry.
