Smoothed particle hydrodynamics（SPH） method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle ...Smoothed particle hydrodynamics（SPH） method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse（mother） particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics（SPH）method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse（mother）particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.展开更多
When a ship sails at high speed,breaking bow waves are formed at the bow,resulting in the component of ship resistance associated with wave-breaking-induced energy dissipation and air entrainment.In this paper,we prop...When a ship sails at high speed,breaking bow waves are formed at the bow,resulting in the component of ship resistance associated with wave-breaking-induced energy dissipation and air entrainment.In this paper,we propose a multi-resolution multi-graphics processing unit two-phase smoothed particle hydrodynamics(SPH)method to simulate the breaking bow waves of a KRISO Container Ship(KCS)model at different Froude numbers.Simulations of five different Froude numbers(Fr=0.377,0.400,0.424,0.450,0.470)are carried out.The total number of particles reaches 1.1×10^(8).The computed wave elevations are compared with the experimental results,which were obtained with the KCS model in a circulating water channel using a binocular stereo reconstruction method.A good agreement is found.The mean wave elevation and its standard deviation,the velocity field,and the vortex structures are analyzed.The results show that increasing the Froude number can lead to more intense fluctuations in wave elevation.The breaking bow waves at the first two Froude numbers are classified as spilling breakers,while those at the last three Froude numbers are plunging breakers.The area of the cavity formed at the impact cross-section increases with the increase of the Froude number.Three main vortex structures are identified for plunging breakers.Vorticity is distributed at the wave crest for spilling breakers,while for plunging breakers,a significant amount of vorticity is found around the cavity.展开更多
基金supported by the National Natural Science Foundation of China (Grant 51609049)the Science Foundation of Heilongjiang Province (Grant QC2016061)the Fundamental Research Funds for the Central Universities (Grants HEUGIP201701,HEUCFJ170109)
文摘Smoothed particle hydrodynamics（SPH） method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse（mother） particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process,conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.Smoothed particle hydrodynamics（SPH）method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems.However,in most simulations,uniform particle distributions are used and the multi-resolution,which can obviously improve the local accuracy and the overall computational efficiency,has seldom been applied.In this paper,a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems.The splitting algorithm is that,when a coarse（mother）particle enters the splitting region,it will be split into four daughter particles,which inherit the physical parameters of the mother particle.In the particle splitting process,conservations of mass,momentum and energy are ensured.Based on the error analysis,the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases.Finally,the scheme is validated by five basic cases,which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems.
基金Project supported by the National Natural Science Foundation of China(Grant No.U22B6010).
文摘When a ship sails at high speed,breaking bow waves are formed at the bow,resulting in the component of ship resistance associated with wave-breaking-induced energy dissipation and air entrainment.In this paper,we propose a multi-resolution multi-graphics processing unit two-phase smoothed particle hydrodynamics(SPH)method to simulate the breaking bow waves of a KRISO Container Ship(KCS)model at different Froude numbers.Simulations of five different Froude numbers(Fr=0.377,0.400,0.424,0.450,0.470)are carried out.The total number of particles reaches 1.1×10^(8).The computed wave elevations are compared with the experimental results,which were obtained with the KCS model in a circulating water channel using a binocular stereo reconstruction method.A good agreement is found.The mean wave elevation and its standard deviation,the velocity field,and the vortex structures are analyzed.The results show that increasing the Froude number can lead to more intense fluctuations in wave elevation.The breaking bow waves at the first two Froude numbers are classified as spilling breakers,while those at the last three Froude numbers are plunging breakers.The area of the cavity formed at the impact cross-section increases with the increase of the Froude number.Three main vortex structures are identified for plunging breakers.Vorticity is distributed at the wave crest for spilling breakers,while for plunging breakers,a significant amount of vorticity is found around the cavity.
