For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of...For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of the Green function directly, a fast approximation method for the Green function is developed by use of Chebyshev polynomials. Examinations are carried out of the accuracy of the Green function and its derivatives from the scheme. It is shown that when an appropriate number of polynomial terms are used, very accurate approximation can be obtained.展开更多
Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G...Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.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
This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary eleme...This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.展开更多
Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
Experimental observations indicate that electromagnetic (EM) radiation is emitted after the detonation of high explosives (HE) charges. The movement of ionized atoms, particles and electrons seems to be the underlying...Experimental observations indicate that electromagnetic (EM) radiation is emitted after the detonation of high explosives (HE) charges. The movement of ionized atoms, particles and electrons seems to be the underlying cause. Expansion of the detonation products (DP) drives a strong (~1 kb) shock in surrounding air. This forms an intense thermal wave (T ~11,000 K) with duration of ~20 microseconds. Such temperatures create significant ionization of the air. According to Ohm’s Law, movement of ionized patches generates current;and according to the Biot-Savart Law, such currents induce electric and magnetic fields. We investigate these effects through numerical simulations of TNT explosions. A high-order Godunov scheme is used to integrate the one-dimensional conservation laws of gasdynamics. An extremely fine grid (10 microns) was needed to get converged temperature and conductivity profiles. The gasdynamic solution provided a source current, which was fed into a time-domain Green’s function code to predict three-dimensional electromagnetic waves emanating from the TNT explosion. This analysis clearly demonstrates one mechanism—the Boronin current—as the source of EM emissions from TNT explosions, but other mechanisms are also possible.展开更多
The time-domain calculations of retard function and ship motions in waves by the direct time-domain method （DTM） and the frequency to time-domain transformation method （FTTM） are compared and analyzed. A Wigley-hu...The time-domain calculations of retard function and ship motions in waves by the direct time-domain method （DTM） and the frequency to time-domain transformation method （FTTM） are compared and analyzed. A Wigley-hull-form ship and an $60 ship moving in waves are examined, and the corresponding retard functions are in good agreement with those given by DTM and FTTM. The comparison of retard functions in different forward speeds by the two methods is observed, and the results of ship motions in forward speed are also compared with the experimental data. On this basis, the advantage and disadvantage of them are discussed.展开更多
Based on the Laplace transform an ordinary differential equation for the two-dimensional time-domain free-surface Green function in ship hydrodynamics is presented. The results for 2D Green function and its horizontal...Based on the Laplace transform an ordinary differential equation for the two-dimensional time-domain free-surface Green function in ship hydrodynamics is presented. The results for 2D Green function and its horizontal derivative are fifth-order ODEs and the vertical derivative satisfies a fourth-order ODE. All of these results may be used to accelerate the numerical computations for the time-domain BEM in marine hydrodynamics.展开更多
文摘For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of the Green function directly, a fast approximation method for the Green function is developed by use of Chebyshev polynomials. Examinations are carried out of the accuracy of the Green function and its derivatives from the scheme. It is shown that when an appropriate number of polynomial terms are used, very accurate approximation can be obtained.
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.
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.
文摘This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
文摘Experimental observations indicate that electromagnetic (EM) radiation is emitted after the detonation of high explosives (HE) charges. The movement of ionized atoms, particles and electrons seems to be the underlying cause. Expansion of the detonation products (DP) drives a strong (~1 kb) shock in surrounding air. This forms an intense thermal wave (T ~11,000 K) with duration of ~20 microseconds. Such temperatures create significant ionization of the air. According to Ohm’s Law, movement of ionized patches generates current;and according to the Biot-Savart Law, such currents induce electric and magnetic fields. We investigate these effects through numerical simulations of TNT explosions. A high-order Godunov scheme is used to integrate the one-dimensional conservation laws of gasdynamics. An extremely fine grid (10 microns) was needed to get converged temperature and conductivity profiles. The gasdynamic solution provided a source current, which was fed into a time-domain Green’s function code to predict three-dimensional electromagnetic waves emanating from the TNT explosion. This analysis clearly demonstrates one mechanism—the Boronin current—as the source of EM emissions from TNT explosions, but other mechanisms are also possible.
文摘The time-domain calculations of retard function and ship motions in waves by the direct time-domain method （DTM） and the frequency to time-domain transformation method （FTTM） are compared and analyzed. A Wigley-hull-form ship and an $60 ship moving in waves are examined, and the corresponding retard functions are in good agreement with those given by DTM and FTTM. The comparison of retard functions in different forward speeds by the two methods is observed, and the results of ship motions in forward speed are also compared with the experimental data. On this basis, the advantage and disadvantage of them are discussed.
文摘Based on the Laplace transform an ordinary differential equation for the two-dimensional time-domain free-surface Green function in ship hydrodynamics is presented. The results for 2D Green function and its horizontal derivative are fifth-order ODEs and the vertical derivative satisfies a fourth-order ODE. All of these results may be used to accelerate the numerical computations for the time-domain BEM in marine hydrodynamics.
