Direct time-domain simulation of floating structures has advantages:it can calculate wave pressure fields and forces directly; and it is useful for coupled analysis of floating structures with a mooring system. A time...Direct time-domain simulation of floating structures has advantages:it can calculate wave pressure fields and forces directly; and it is useful for coupled analysis of floating structures with a mooring system. A time-domain boundary integral equation method is presented to simulate three-dimensional water wave radiation problems. A stable form of the integration free-surface boundary condition (IFBC) is used to update velocity potentials on the free surface. A multi-transmitting formula (MTF) method with an artificial speed is introduced to the artificial radiation boundary (ARB). The method was applied to simulate a semi-spherical liquefied natural gas (LNG) carrier and a semi-submersible undergoing specified harmonic motion. Numerical parameters such as the form of the ARB, and the time and space discretization related to this method are discussed. It was found that a good agreement can be obtained when artificial speed is between 0.6 and 1.6 times the phase velocity of water waves in the MTF method. A simulation can be done for a long period of time by this method without problems of instability, and the method is also accurate and computationally efficient.展开更多
This paper focuses on the research of a semi-submersible platform equipped with a DP-assisted mooring system. Based on the working principles of the DP-assisted mooring system and the model of the platform motion, a t...This paper focuses on the research of a semi-submersible platform equipped with a DP-assisted mooring system. Based on the working principles of the DP-assisted mooring system and the model of the platform motion, a time domain simulation program is applied to analyze the impact, in the case of one line failure, on the platform motion, power consumption of the thrusters and the tension of the mooring lines. The results show that, under the 10-year wind dominant, a one line failure will have little impact on the tension of the mooring lines. When the failure line is windward, the power consumption will increase greatly with a weakened position of accuracy. However when the failure line is leeward, the power consumption will be reduced with a partly strengthened oosition of accuracy.展开更多
Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity ...Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.展开更多
Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular w...Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.展开更多
The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-die...The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-dielectric slab is investigated by using the three-dimensional finite-difference time-domain method （3D-FDTD） with different slotantenna structures. And the experimental image of discharge with a novel slot antenna array and the simulation of the electric field with this slot antenna array are both displayed. Combined with the distribution of surface wave excitation and experimental results, the numerical simulation performed by using 3D-FDTD is shown to be a useful tool in the computer-aided antenna design for large area planar-type surface-wave plasma sources.展开更多
A new thin film pulse transformer for using in ISND and ADSL systems has been designed based on a domain wall pinning model, the parameters of nano-magnetic thin film such as permeability and coercivity can be calcula...A new thin film pulse transformer for using in ISND and ADSL systems has been designed based on a domain wall pinning model, the parameters of nano-magnetic thin film such as permeability and coercivity can be calculated. The main properties of the thin film transformer including the size, parallel inductance, Q value and turn ratio have been simulated and optimized. Simulation results show that the thin film transformer can be fairly operated in a frequency range of 0.001~20 MHz.展开更多
The evolution process of magnetic domains in response to external fields is crucial for the modern understanding and application of spintronics.In this study,we investigated the domain rotation in stripe domain films ...The evolution process of magnetic domains in response to external fields is crucial for the modern understanding and application of spintronics.In this study,we investigated the domain rotation in stripe domain films of varying thicknesses by examining their response to microwave excitation in four different orientations.The resonance spectra indicate that the rotation field of stripe domain film under an applied magnetic field approaches the field where the resonance mode of sample changes.The saturation field of the stripe domain film corresponds to the field where the resonance mode disappears when measured in the stripe direction parallel to the microwave magnetic field.The results are reproducible and consistent with micromagnetic simulations,providing additional approaches and techniques for comprehending the microscopic mechanisms of magnetic domains and characterizing their rotation.展开更多
Investigations on domain wall(DW) and spin wave(SW) modes in a series of nanostrips with different widths and thicknesses have been carried out using micromagnetic simulation. The simulation results show that the freq...Investigations on domain wall(DW) and spin wave(SW) modes in a series of nanostrips with different widths and thicknesses have been carried out using micromagnetic simulation. The simulation results show that the frequencies of SW modes and the corresponding DW modes are consistent with each other if they have the same node number along the width direction. This consistency is more pronounced in wide and thin nanostrips, favoring the DW motion driven by SWs.Further analysis of the moving behavior of a DW driven by SWs is also carried out. The average DW speed can reach a larger value of ~ 140 m/s under two different SW sources. We argue that this study is very meaningful for the potential application of DW motion driven by SWs.展开更多
Most of the reported observations are about the dynamic properties of individual domain-walls in magnetic nanowires,but the properties of multiple stripe-domains have rarely been investigated.Here,we demonstrate a sim...Most of the reported observations are about the dynamic properties of individual domain-walls in magnetic nanowires,but the properties of multiple stripe-domains have rarely been investigated.Here,we demonstrate a simple but efficient scenario for multiple domains injection in magnetic nanowires.The domain-chains(DCs),a cluster of multiple domains,can be dynamically generated with tunable static properties.It is found that the number of domains in a single DC can be dynamically adjusted by varying the frequency of microwave field(MF)and the period of spin-polarized current(SPC)intensity.The static properties of the DCs,i.e.,its length,spacing,and period between neighboring DCs,can be dynamically controlled by regulating the frequency of MF and the intensity of SPC.We have also discussed the possibility of using domain-chains as information carries,which provides a meaningful approach for flexible multi-bit information storage applications.展开更多
The switching behavior of antiferroelectric domain structures under the applied electric field is not fully understood.In this work,by using the phase field simulation,we have studied the polarization switching proper...The switching behavior of antiferroelectric domain structures under the applied electric field is not fully understood.In this work,by using the phase field simulation,we have studied the polarization switching property of antiferroelectric domains.Our results indicate that the ferroelectric domains nucleate preferably at the boundaries of the antiferroelectric domains,and antiferroelectrics with larger initial domain sizes possess a higher coercive electric field as demonstrated by hysteresis loops.Moreover,we introduce charge defects into the sample and numerically investigate their influence.It is also shown that charge defects can induce local ferroelectric domains,which could suppress the saturation polarization and narrow the enclosed area of the hysteresis loop.Our results give insights into understanding the antiferroelectric phase transformation and optimizing the energy storage property in experiments.展开更多
A vortex domain wall's(VW) magnetic racetrack memory's high performance depends on VW structural stability,high speed, low power consumption and high storage density. In this study, these critical parameters w...A vortex domain wall's(VW) magnetic racetrack memory's high performance depends on VW structural stability,high speed, low power consumption and high storage density. In this study, these critical parameters were investigated in magnetic multi-segmented nanowires using micromagnetic simulation. Thus, an offset magnetic nanowire with a junction at the center was proposed for this purpose. This junction was implemented by shifting one portion of the magnetic nanowire horizontally in the x-direction(l) and vertically(d) in the y-direction. The VW structure became stable by manipulating magnetic properties, such as magnetic saturation(M_(4)) and magnetic anisotropy energy(K_(u)). In this case, increasing the values of M_(4) ≥ 800 kA/m keeps the VW structure stable during its dynamics and pinning and depinning in offset nanowires,which contributes to maintenance of the storage memory's lifetime for a longer period. It was also found that the VW moved with a speed of 500 m/s, which is desirable for VW racetrack memory devices. Moreover, it was revealed that the VW velocity could be controlled by adjusting the offset area dimensions(l and d), which helps to drive the VW by using low current densities and reducing the thermal-magnetic spin fluctuations. Further, the depinning current density of the VW(J_(d)) over the offset area increases as d increases and l decreases. In addition, magnetic properties, such as the M_(4) and K_(u),can affect the depinning process of the VW through the offset area. For high storage density, magnetic nanowires(multisegmented) with four junctions were designed. In total, six states were found with high VW stability, which means three bits per cell. Herein, we observed that the depinning current density(J_(d)) for moving the VW from one state to another was highly influenced by the offset area geometry(l and d) and the material's magnetic properties, such as the M_(4) and K_(u).展开更多
Several major challenges need to be faced for efficient transient multiscale electromagnetic simulations, such as flex- ible and robust geometric modeling schemes, efficient and stable time-stepping algorithms, etc. F...Several major challenges need to be faced for efficient transient multiscale electromagnetic simulations, such as flex- ible and robust geometric modeling schemes, efficient and stable time-stepping algorithms, etc. Fortunately, because of the versatile choices of spatial discretization and temporal integration, a discontinuous Galerkin time-domain （DGTD） method can be a very promising method of solving transient multiscale electromagnetic problems. In this paper, we present the application of a leap-frog DGTD method to the analyzing of the multiscale electromagnetic scattering problems. The uniaxial perfect matching layer （UPML） truncation of the computational domain is discussed and formulated in the leap-frog DGTD context. Numerical validations are performed in the challenging test cases demonstrating the accuracy and effectiveness of the method in solving transient multiscale electromagnetic problems compared with those of other numerical methods.展开更多
Strong hydrodynamic interactions during the side-by-side offloading operation between floating liquefied natural gas(FLNG) and liquefied natural gas carrier(LNGC) can induce high risks of collision. The weather vane e...Strong hydrodynamic interactions during the side-by-side offloading operation between floating liquefied natural gas(FLNG) and liquefied natural gas carrier(LNGC) can induce high risks of collision. The weather vane effect of a single-point mooring system normally results in the satisfactory hydrodynamic performance of the side-by-side configuration in head seas. Nevertheless, the changes in wave directions in real sea conditions can significantly influence the relative motions. This article studies the relative motions of the side-by-side system by using the theoretical analysis method and the numerical calculation method. Based on the three-dimensional potential theory modified by artificial damping-lid method, the frequency-domain hydrodynamic coefficients can be improved to calculate the retardation functions for the multi-body problem. An in-house code is then developed to perform the time-domain simulation of two vessels, through which the relative motions are subsequently obtained. A range of oblique waves are chosen for the extensive calculation of relative motions between the two vessels, which are further analyzed in terms of the phase shift of motion responses induced by specific resonant wave patterns. Investigation results show that wave directions have a significant influence on the relative sway, roll, and yaw motions. Under the circumstance that the absolute phase shift between the roll motions of two vessels approaches 180°, stronger relative motions are induced when LNGC is on the weather side.Moreover, the gap water resonances at high frequencies tend to cause the dangerous opposed oscillation of two vessels in the sway and yaw modes, whereas FLNG reduces the gap water resonances and relative motions when located on the weather side.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10572041,50779008 and the 111 Project
文摘Direct time-domain simulation of floating structures has advantages:it can calculate wave pressure fields and forces directly; and it is useful for coupled analysis of floating structures with a mooring system. A time-domain boundary integral equation method is presented to simulate three-dimensional water wave radiation problems. A stable form of the integration free-surface boundary condition (IFBC) is used to update velocity potentials on the free surface. A multi-transmitting formula (MTF) method with an artificial speed is introduced to the artificial radiation boundary (ARB). The method was applied to simulate a semi-spherical liquefied natural gas (LNG) carrier and a semi-submersible undergoing specified harmonic motion. Numerical parameters such as the form of the ARB, and the time and space discretization related to this method are discussed. It was found that a good agreement can be obtained when artificial speed is between 0.6 and 1.6 times the phase velocity of water waves in the MTF method. A simulation can be done for a long period of time by this method without problems of instability, and the method is also accurate and computationally efficient.
基金Suppirted by the Programme of Introducing Talents of Discipline to Universities(B07019)
文摘This paper focuses on the research of a semi-submersible platform equipped with a DP-assisted mooring system. Based on the working principles of the DP-assisted mooring system and the model of the platform motion, a time domain simulation program is applied to analyze the impact, in the case of one line failure, on the platform motion, power consumption of the thrusters and the tension of the mooring lines. The results show that, under the 10-year wind dominant, a one line failure will have little impact on the tension of the mooring lines. When the failure line is windward, the power consumption will increase greatly with a weakened position of accuracy. However when the failure line is leeward, the power consumption will be reduced with a partly strengthened oosition of accuracy.
基金funded by the National Natural Science Foundation of China(Grant No.52274048)Beijing Natural Science Foundation(Grant No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(Grant No.2021DJ2104)the Science Foundation of China University of Petroleum-Beijing(No.2462021YXZZ010).
文摘Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.
基金the National Key R&D Program of China (Grant No.2016YFE0200100)the National Natural Science Foundation of China (Grant Nos.51490672 and 51479026).
文摘Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.
基金supported by the Foundation for Returned Scholars,the Ministry of Education of China
文摘The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-dielectric slab is investigated by using the three-dimensional finite-difference time-domain method （3D-FDTD） with different slotantenna structures. And the experimental image of discharge with a novel slot antenna array and the simulation of the electric field with this slot antenna array are both displayed. Combined with the distribution of surface wave excitation and experimental results, the numerical simulation performed by using 3D-FDTD is shown to be a useful tool in the computer-aided antenna design for large area planar-type surface-wave plasma sources.
文摘A new thin film pulse transformer for using in ISND and ADSL systems has been designed based on a domain wall pinning model, the parameters of nano-magnetic thin film such as permeability and coercivity can be calculated. The main properties of the thin film transformer including the size, parallel inductance, Q value and turn ratio have been simulated and optimized. Simulation results show that the thin film transformer can be fairly operated in a frequency range of 0.001~20 MHz.
基金the Natural Science Foundation of Shandong Province(Grant No.ZR2022MA053),the National Natural Science Foundation of China(Grant Nos.11704211,11847233,52301255,12205157,and 12205093)the Funda-mental Research Funds for the Central Universities(Grant No.lzujbky-2022-kb01)+2 种基金China and Germany Postdoctoral Exchange Program(Helmholtz-OCPC)China Postdoctoral Science Foundation(Grant No.2018M632608)Applied Basic Research Project of Qingdao(Grant No.18-2-2-16-jcb).
文摘The evolution process of magnetic domains in response to external fields is crucial for the modern understanding and application of spintronics.In this study,we investigated the domain rotation in stripe domain films of varying thicknesses by examining their response to microwave excitation in four different orientations.The resonance spectra indicate that the rotation field of stripe domain film under an applied magnetic field approaches the field where the resonance mode of sample changes.The saturation field of the stripe domain film corresponds to the field where the resonance mode disappears when measured in the stripe direction parallel to the microwave magnetic field.The results are reproducible and consistent with micromagnetic simulations,providing additional approaches and techniques for comprehending the microscopic mechanisms of magnetic domains and characterizing their rotation.
基金Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 20720210030)the National Natural Science Foundation of China (Grant No. 11204255)。
文摘Investigations on domain wall(DW) and spin wave(SW) modes in a series of nanostrips with different widths and thicknesses have been carried out using micromagnetic simulation. The simulation results show that the frequencies of SW modes and the corresponding DW modes are consistent with each other if they have the same node number along the width direction. This consistency is more pronounced in wide and thin nanostrips, favoring the DW motion driven by SWs.Further analysis of the moving behavior of a DW driven by SWs is also carried out. The average DW speed can reach a larger value of ~ 140 m/s under two different SW sources. We argue that this study is very meaningful for the potential application of DW motion driven by SWs.
基金Project supported by the National Natural Science Foundation of China(Grant No.11704191)the Jiangsu Specially-Appointed Professor,the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20171026)the Six-Talent Peaks Project in Jiangsu Province,China(Grant No.XYDXX-038)
文摘Most of the reported observations are about the dynamic properties of individual domain-walls in magnetic nanowires,but the properties of multiple stripe-domains have rarely been investigated.Here,we demonstrate a simple but efficient scenario for multiple domains injection in magnetic nanowires.The domain-chains(DCs),a cluster of multiple domains,can be dynamically generated with tunable static properties.It is found that the number of domains in a single DC can be dynamically adjusted by varying the frequency of microwave field(MF)and the period of spin-polarized current(SPC)intensity.The static properties of the DCs,i.e.,its length,spacing,and period between neighboring DCs,can be dynamically controlled by regulating the frequency of MF and the intensity of SPC.We have also discussed the possibility of using domain-chains as information carries,which provides a meaningful approach for flexible multi-bit information storage applications.
基金Project supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20190405)the LOEWE program of the State of Hesse,Germany,within the project FLAME(Fermi Level Engineering of Antiferroelectric Materials for Energy Storage and Insulation Systems)。
文摘The switching behavior of antiferroelectric domain structures under the applied electric field is not fully understood.In this work,by using the phase field simulation,we have studied the polarization switching property of antiferroelectric domains.Our results indicate that the ferroelectric domains nucleate preferably at the boundaries of the antiferroelectric domains,and antiferroelectrics with larger initial domain sizes possess a higher coercive electric field as demonstrated by hysteresis loops.Moreover,we introduce charge defects into the sample and numerically investigate their influence.It is also shown that charge defects can induce local ferroelectric domains,which could suppress the saturation polarization and narrow the enclosed area of the hysteresis loop.Our results give insights into understanding the antiferroelectric phase transformation and optimizing the energy storage property in experiments.
文摘A vortex domain wall's(VW) magnetic racetrack memory's high performance depends on VW structural stability,high speed, low power consumption and high storage density. In this study, these critical parameters were investigated in magnetic multi-segmented nanowires using micromagnetic simulation. Thus, an offset magnetic nanowire with a junction at the center was proposed for this purpose. This junction was implemented by shifting one portion of the magnetic nanowire horizontally in the x-direction(l) and vertically(d) in the y-direction. The VW structure became stable by manipulating magnetic properties, such as magnetic saturation(M_(4)) and magnetic anisotropy energy(K_(u)). In this case, increasing the values of M_(4) ≥ 800 kA/m keeps the VW structure stable during its dynamics and pinning and depinning in offset nanowires,which contributes to maintenance of the storage memory's lifetime for a longer period. It was also found that the VW moved with a speed of 500 m/s, which is desirable for VW racetrack memory devices. Moreover, it was revealed that the VW velocity could be controlled by adjusting the offset area dimensions(l and d), which helps to drive the VW by using low current densities and reducing the thermal-magnetic spin fluctuations. Further, the depinning current density of the VW(J_(d)) over the offset area increases as d increases and l decreases. In addition, magnetic properties, such as the M_(4) and K_(u),can affect the depinning process of the VW through the offset area. For high storage density, magnetic nanowires(multisegmented) with four junctions were designed. In total, six states were found with high VW stability, which means three bits per cell. Herein, we observed that the depinning current density(J_(d)) for moving the VW from one state to another was highly influenced by the offset area geometry(l and d) and the material's magnetic properties, such as the M_(4) and K_(u).
基金supported by the National Natural Science Foundation of China(Grant Nos.61301056 and 11176007)the Sichuan Provincial Science and Technology Support Program,China(Grant No.2013HH0047)+1 种基金the Fok Ying Tung Education Foundation,China(Grant No.141062)the"111"Project,China(Grant No.B07046)
文摘Several major challenges need to be faced for efficient transient multiscale electromagnetic simulations, such as flex- ible and robust geometric modeling schemes, efficient and stable time-stepping algorithms, etc. Fortunately, because of the versatile choices of spatial discretization and temporal integration, a discontinuous Galerkin time-domain （DGTD） method can be a very promising method of solving transient multiscale electromagnetic problems. In this paper, we present the application of a leap-frog DGTD method to the analyzing of the multiscale electromagnetic scattering problems. The uniaxial perfect matching layer （UPML） truncation of the computational domain is discussed and formulated in the leap-frog DGTD context. Numerical validations are performed in the challenging test cases demonstrating the accuracy and effectiveness of the method in solving transient multiscale electromagnetic problems compared with those of other numerical methods.
基金supported by the China National Scientific and Technology Major Project(2016ZX05028-002-004)
文摘Strong hydrodynamic interactions during the side-by-side offloading operation between floating liquefied natural gas(FLNG) and liquefied natural gas carrier(LNGC) can induce high risks of collision. The weather vane effect of a single-point mooring system normally results in the satisfactory hydrodynamic performance of the side-by-side configuration in head seas. Nevertheless, the changes in wave directions in real sea conditions can significantly influence the relative motions. This article studies the relative motions of the side-by-side system by using the theoretical analysis method and the numerical calculation method. Based on the three-dimensional potential theory modified by artificial damping-lid method, the frequency-domain hydrodynamic coefficients can be improved to calculate the retardation functions for the multi-body problem. An in-house code is then developed to perform the time-domain simulation of two vessels, through which the relative motions are subsequently obtained. A range of oblique waves are chosen for the extensive calculation of relative motions between the two vessels, which are further analyzed in terms of the phase shift of motion responses induced by specific resonant wave patterns. Investigation results show that wave directions have a significant influence on the relative sway, roll, and yaw motions. Under the circumstance that the absolute phase shift between the roll motions of two vessels approaches 180°, stronger relative motions are induced when LNGC is on the weather side.Moreover, the gap water resonances at high frequencies tend to cause the dangerous opposed oscillation of two vessels in the sway and yaw modes, whereas FLNG reduces the gap water resonances and relative motions when located on the weather side.
