基于大涡模拟的移动粒子半隐式法研究及其应用
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摘要
自由表面是船舶与海洋工程领域的一个重要研究课题,对自由表面问题的模拟是船舶与海洋工程领域,计算流体力学的难点之一。虽然一些基于欧拉网格的自由表面处理方法在模拟带自由表面问题时能够取得不错的结果,但当遇到大变形自由表面、液面破碎、飞溅等问题时,基于欧拉网格的数值方法将使计算量增加并会遇到一定困难。移动粒子半隐式法(Moving-Particle Semi-Implicit Method, MPS)是最近兴起的一种基于拉格朗日(Lagrange)粒子的无网格法, MPS法中粒子的运动性使得该方法在自由表面尤其是大变形自由表面的模拟中有着出色的表现。研究表明,MPS法在船舶与海洋工程领域有着广阔的应用前景,但是鉴于该方法提出不久,算法自身仍有一些缺陷制约着MPS法的发展。因此,本文的目的在于研究MPS法理论基础,针对该方法目前比较突出的几点不足之处,讨论缓解或解决这些缺点的方法,进一步完善MPS法的理论,使其在船舶与海洋工程领域有着更好的适应能力,最后再结合大涡模拟,将MPS法应用至具有大变形自由表面的液体晃荡问题中。本文主要有以下几点内容和创新点:
一、使用了一种防止粒子碰撞或穿越的人工修正步。MPS法中的拉格朗日粒子有着很强的运动随机性,使得在模拟过程中粒子之间相互碰撞以及粒子穿越边界条件的情况频繁发生,通过使用该人工修正步以避免上述情况的发生。数值实验表明,使用了该人工修正步后,模拟可以顺利进行,合适的修正距离可以保证粒子碰撞或穿越现象在整个模拟中出现的概率极低。
二、讨论了不同核函数在不同类型模拟中的适用性。核函数是MPS法中的重要参数,也是MPS法中为数不多的可调参数之一,以往的研究中,往往通过调整不同的核函数来获取更好的模拟结果,但是没有针对核函数的特性进行系统的研究。通过讨论不同核函数在不同类型模拟中的适用性,可以指导在不同模拟中核函数的选取情况。
三、研究了压力振荡现象,提出了以面积-时间平均为扩展的缓解方法,讨论了该方法对压力振荡现象的缓解效果。长期以来,压力振荡现象一直是制约MPS法广泛应用的最大原因,在早期MPS法的研究中,大多的注意力放在自由表面的表现上,压力问题因振荡现象而被忽视。通过使用面积-时间平均法,对不同的面积平均方式和不同的时间平均段进行讨论,选取合适的面积-时间平均方法,可将MPS法的压力结果缓解至工程实践可接受的范围之内,这为MPS法的进一步应用做好了准备,并且基于面积-时间的压力平均法也符合MPS法理论的实际意义。
四、提出一种全新的基于邻居搜索的自由表面混合判别方法。通过粒子数密度来判别自由表面是MPS法在自由表面处理上的一大特色,该自由表面判别方法不但物理意义明确,而且基本不消耗计算资源,有着极高的效率。但是由于MPS法的算法流程问题,该方法会不可避免的产生自由表面的误判情况,这样不但会给模拟结果带来误差,还会加重模拟中的压力振荡现象,实际模拟表明这种自由表面误判的情况较为严重。新的自由表面判别方法由于是基于邻居搜索的,既而可以避免误判情况的发生,考虑到使用粒子数密度来判别自由表面的方法有着很高的效率,所以将基于邻居搜索的自由表面判别方法同基于数密度的自由表面判别方法结合使用,只在自由表面误判较为频繁的粒子数密度段使用邻居搜索,这样在不影响模拟效率的前提下,很大程度上避免了非自由表面粒子被误判的情况发生。
五、基于大涡模拟的MPS法在具有大变形自由表面晃荡问题中的应用。工程中大部分问题都是湍流问题,而以往绝大多数的MPS法研究中均未考虑湍流,所以实现MPS的大涡模拟有着积极的意义。论文通过Smagorinsky涡粘模型,实现了MPS法的大涡模拟,讨论了大涡模拟中微分模型的合适作用距离。最后结合之前提出的方法,成功的模拟了3种不同情况下,具有大变形自由表面的晃荡问题,包括在二维水平方向上晃荡的共振方形液箱,二维平面内横摇的模型化的共振LNG液舱,以及在二维平面内3方向耦合运动的全尺寸共振LNG棱柱形液舱。上述不同方法在模拟中同时应用,均有很好的表现,模拟能够得到满意的结果。
在具体的使用中,人工修正步能够很好的避免模拟中的碰撞和穿越问题;不同核函数的适用性能够准确的指导不同类型模拟的核函数选取;基于邻居搜索的混合自由表面判别方法能够准确的识别自由表面,并且对模拟的效率整体影响不大;而基于面积-时间平均的压力振荡缓解方法可以得到很好的压力结果,将原MPS法完全不能使用,幅度极大的振荡结果缓解至工程上可接受范围之内,并且压力结果同实验结果、其他数值模拟结果都极为接近,在晃荡的拍击压力上也有不错的表现。
实践证明,提出的新技术或方法能够适应于MPS法的应用,并且很好的弥补了原MPS法在相关方面的不足。另外经过进一步完善MPS法大涡在大变形自由表面晃荡问题中有良好的表现,能够模拟出各种物理现象,这对工程实践有着重要的指导意义。
Modeling free surface flows is of great significance in the field of ship and ocean engineering. However, these flows are difficult to simulate because the surface boundary conditions are specified on arbitarity moving surface. Some methods in Eulerian grid are flexible and robust to trace free surface in simulation, but with those method, Navier-Stokes equations are solved on a fixed grid, which brings the problem of numerical diffusion because the existence of the advection term in Navier-Stokes equations, especially when the deformation of free surface is very large and complicated or the free surface splashes. Moving-Particle Semi-Implicit Method (MPS) is a new meshless numerical method which bases on Lagrange particle, due to the advantage in free surface simulation, the MPS method plays more and more important role in numerical research. Studies show that the MPS method has broad prospects in the area of Naval Architecture and Ocean Engineering. But there are some deficiencies in its theory to restrict the development of MPS method. This paper studies deficiencies of MPS theory, and proposes some technologies for these deficiencies. With these technologies, the MPS method is coupled with a sub-particle scale (SPS) turbulence model to simulate sloshing problems with large deforming free surface. This paper has the following content andinnovations:
1. Additional correction term for particles collision or pass through phenomena. Because the Lagrange behavior of particles, there are lots of particles collision phenomena in MPS simulation, some of these collision phenomena will pass through the boundary and lead to a serious consequence, but with the additional correction term and appropriate distance for correction, there are only few particles collision phenomena in simulations, and the probability of pass through phenomena is few.
2. Behavior of kernel function in MPS method. Kernel function is a very important part in MPS theory, and it is one of the only a few adjustable parameters in MPS method. In early studies, better results are got by adjust kernel functions, but there has no systemic study on kerner functions’behavior. So the study on behavior of kernel function can help to select the kernel function for simulations.
3. Pressure fluctuation phenomena, an area-time average method for pressure fluctuation phenomena, and the effect of the area-time average method. The unacceptable pressure fluctuation is an obvious defect in MPS method, and it has a negative influence to the development of MPS method. In most studies by MPS, more attention are putted on the free surface, pressure results are neglected because the fluctuation. An area-time average method is proposed in this paper, different area average type and different time average period are discussed. With different area-time average methods, the fluctuation of pressure is solved, the result is quit good and acceptable, and that makes MPS method more suitable for ocean engineering problem.
4. A new mixed free surface traced method for MPS method, which based on neighbors search. MPS method uses the numerical density to trace the free surface, and it is efficiency. But due to the algorithm of MPS method, there are lots of non-free surface particles are traced as free surface particles. That will cause mistakes in simulation and make the pressure fluctuation more serious. The new mixed free surface traced method bases on neighbors search, so it solves the mistreatment problem in theory. Because its efficiency to use numerical density for free surface, the neighbors search method is mixed used with numerical density method, the neighbors search method is used when the mistreatment problem always happen, so the mixed free surface traced method solved the mistreatment problem with efficiency.
5. Modified MPS-LES method for sloshing problem with violent surface. Most ocean engineering problems are problems with turbulence flow, and most of the early studies which bases on MPS method are laminar flow, so it is meanful to simulate the practical cases with turbulent flow. In this paper, the MPS method is extended to the large eddy simulation (LES) by coupled with a sub-particle-scale (SPS) turbulence model, the effect of the SPS turbulence is found as the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. 3 different sloshing problems are simulated by MPS-LES method successfully, these cases are a resonance sloshing rectangular tank, a modeled resonance rolling LNG tank longitudinal section and a full-scale resonance mix movement LNG tank transverse section.
Results show, these new technologies or methods adapted to the MPS method and improved the original one. With these technologies, the modified MPS-LES method is good at the simulation of sloshing with large deforming free surface. The additional correction term make the modified MPS-LES method avoided nearly the entire pass through phenomena; behavior of kernel function is helpful to select a kernel function before simulation; the new mixed free surface traced method work well and no more mistreatment; different area-time average methods solved pressure fluctuation well, the pressure is good and very close to pressure of experiments or pressure by other methods.
一、使用了一种防止粒子碰撞或穿越的人工修正步。MPS法中的拉格朗日粒子有着很强的运动随机性,使得在模拟过程中粒子之间相互碰撞以及粒子穿越边界条件的情况频繁发生,通过使用该人工修正步以避免上述情况的发生。数值实验表明,使用了该人工修正步后,模拟可以顺利进行,合适的修正距离可以保证粒子碰撞或穿越现象在整个模拟中出现的概率极低。
二、讨论了不同核函数在不同类型模拟中的适用性。核函数是MPS法中的重要参数,也是MPS法中为数不多的可调参数之一,以往的研究中,往往通过调整不同的核函数来获取更好的模拟结果,但是没有针对核函数的特性进行系统的研究。通过讨论不同核函数在不同类型模拟中的适用性,可以指导在不同模拟中核函数的选取情况。
三、研究了压力振荡现象,提出了以面积-时间平均为扩展的缓解方法,讨论了该方法对压力振荡现象的缓解效果。长期以来,压力振荡现象一直是制约MPS法广泛应用的最大原因,在早期MPS法的研究中,大多的注意力放在自由表面的表现上,压力问题因振荡现象而被忽视。通过使用面积-时间平均法,对不同的面积平均方式和不同的时间平均段进行讨论,选取合适的面积-时间平均方法,可将MPS法的压力结果缓解至工程实践可接受的范围之内,这为MPS法的进一步应用做好了准备,并且基于面积-时间的压力平均法也符合MPS法理论的实际意义。
四、提出一种全新的基于邻居搜索的自由表面混合判别方法。通过粒子数密度来判别自由表面是MPS法在自由表面处理上的一大特色,该自由表面判别方法不但物理意义明确,而且基本不消耗计算资源,有着极高的效率。但是由于MPS法的算法流程问题,该方法会不可避免的产生自由表面的误判情况,这样不但会给模拟结果带来误差,还会加重模拟中的压力振荡现象,实际模拟表明这种自由表面误判的情况较为严重。新的自由表面判别方法由于是基于邻居搜索的,既而可以避免误判情况的发生,考虑到使用粒子数密度来判别自由表面的方法有着很高的效率,所以将基于邻居搜索的自由表面判别方法同基于数密度的自由表面判别方法结合使用,只在自由表面误判较为频繁的粒子数密度段使用邻居搜索,这样在不影响模拟效率的前提下,很大程度上避免了非自由表面粒子被误判的情况发生。
五、基于大涡模拟的MPS法在具有大变形自由表面晃荡问题中的应用。工程中大部分问题都是湍流问题,而以往绝大多数的MPS法研究中均未考虑湍流,所以实现MPS的大涡模拟有着积极的意义。论文通过Smagorinsky涡粘模型,实现了MPS法的大涡模拟,讨论了大涡模拟中微分模型的合适作用距离。最后结合之前提出的方法,成功的模拟了3种不同情况下,具有大变形自由表面的晃荡问题,包括在二维水平方向上晃荡的共振方形液箱,二维平面内横摇的模型化的共振LNG液舱,以及在二维平面内3方向耦合运动的全尺寸共振LNG棱柱形液舱。上述不同方法在模拟中同时应用,均有很好的表现,模拟能够得到满意的结果。
在具体的使用中,人工修正步能够很好的避免模拟中的碰撞和穿越问题;不同核函数的适用性能够准确的指导不同类型模拟的核函数选取;基于邻居搜索的混合自由表面判别方法能够准确的识别自由表面,并且对模拟的效率整体影响不大;而基于面积-时间平均的压力振荡缓解方法可以得到很好的压力结果,将原MPS法完全不能使用,幅度极大的振荡结果缓解至工程上可接受范围之内,并且压力结果同实验结果、其他数值模拟结果都极为接近,在晃荡的拍击压力上也有不错的表现。
实践证明,提出的新技术或方法能够适应于MPS法的应用,并且很好的弥补了原MPS法在相关方面的不足。另外经过进一步完善MPS法大涡在大变形自由表面晃荡问题中有良好的表现,能够模拟出各种物理现象,这对工程实践有着重要的指导意义。
Modeling free surface flows is of great significance in the field of ship and ocean engineering. However, these flows are difficult to simulate because the surface boundary conditions are specified on arbitarity moving surface. Some methods in Eulerian grid are flexible and robust to trace free surface in simulation, but with those method, Navier-Stokes equations are solved on a fixed grid, which brings the problem of numerical diffusion because the existence of the advection term in Navier-Stokes equations, especially when the deformation of free surface is very large and complicated or the free surface splashes. Moving-Particle Semi-Implicit Method (MPS) is a new meshless numerical method which bases on Lagrange particle, due to the advantage in free surface simulation, the MPS method plays more and more important role in numerical research. Studies show that the MPS method has broad prospects in the area of Naval Architecture and Ocean Engineering. But there are some deficiencies in its theory to restrict the development of MPS method. This paper studies deficiencies of MPS theory, and proposes some technologies for these deficiencies. With these technologies, the MPS method is coupled with a sub-particle scale (SPS) turbulence model to simulate sloshing problems with large deforming free surface. This paper has the following content andinnovations:
1. Additional correction term for particles collision or pass through phenomena. Because the Lagrange behavior of particles, there are lots of particles collision phenomena in MPS simulation, some of these collision phenomena will pass through the boundary and lead to a serious consequence, but with the additional correction term and appropriate distance for correction, there are only few particles collision phenomena in simulations, and the probability of pass through phenomena is few.
2. Behavior of kernel function in MPS method. Kernel function is a very important part in MPS theory, and it is one of the only a few adjustable parameters in MPS method. In early studies, better results are got by adjust kernel functions, but there has no systemic study on kerner functions’behavior. So the study on behavior of kernel function can help to select the kernel function for simulations.
3. Pressure fluctuation phenomena, an area-time average method for pressure fluctuation phenomena, and the effect of the area-time average method. The unacceptable pressure fluctuation is an obvious defect in MPS method, and it has a negative influence to the development of MPS method. In most studies by MPS, more attention are putted on the free surface, pressure results are neglected because the fluctuation. An area-time average method is proposed in this paper, different area average type and different time average period are discussed. With different area-time average methods, the fluctuation of pressure is solved, the result is quit good and acceptable, and that makes MPS method more suitable for ocean engineering problem.
4. A new mixed free surface traced method for MPS method, which based on neighbors search. MPS method uses the numerical density to trace the free surface, and it is efficiency. But due to the algorithm of MPS method, there are lots of non-free surface particles are traced as free surface particles. That will cause mistakes in simulation and make the pressure fluctuation more serious. The new mixed free surface traced method bases on neighbors search, so it solves the mistreatment problem in theory. Because its efficiency to use numerical density for free surface, the neighbors search method is mixed used with numerical density method, the neighbors search method is used when the mistreatment problem always happen, so the mixed free surface traced method solved the mistreatment problem with efficiency.
5. Modified MPS-LES method for sloshing problem with violent surface. Most ocean engineering problems are problems with turbulence flow, and most of the early studies which bases on MPS method are laminar flow, so it is meanful to simulate the practical cases with turbulent flow. In this paper, the MPS method is extended to the large eddy simulation (LES) by coupled with a sub-particle-scale (SPS) turbulence model, the effect of the SPS turbulence is found as the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. 3 different sloshing problems are simulated by MPS-LES method successfully, these cases are a resonance sloshing rectangular tank, a modeled resonance rolling LNG tank longitudinal section and a full-scale resonance mix movement LNG tank transverse section.
Results show, these new technologies or methods adapted to the MPS method and improved the original one. With these technologies, the modified MPS-LES method is good at the simulation of sloshing with large deforming free surface. The additional correction term make the modified MPS-LES method avoided nearly the entire pass through phenomena; behavior of kernel function is helpful to select a kernel function before simulation; the new mixed free surface traced method work well and no more mistreatment; different area-time average methods solved pressure fluctuation well, the pressure is good and very close to pressure of experiments or pressure by other methods.
引文
[1]刘应中,张怀新,李谊乐,缪国平. 21世纪的船舶性能计算和RANS方程[J].船舶力学. 2001, 5(5): 66~84.
[2]张雄,宋康祖,陆明万.无网格法研究进展及其应用[J].计算力学学报. 2003, 20(6): 730~742.
[3]贾高顺,王晓光,梁利华,马修彦.无网格方法的应用前景[J].科技通报. 2003, 19(5): 360~364.
[4]李邵武,尹振军. N-S方程的数值解法及其在水波动力学中应用的综述[J].海洋通报. 2004, 23(4): 79~85.
[5]顾元通,丁桦.无网格法及其最新进展[J].力学进展. 2005, 35(3): 323~337.
[6]李九红,程玉明.无网格方法的研究进展与展望[J].力学季刊. 2006, 27(1): 143~152.
[7] Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. Meshless Method: An Overview and Recent Developments[J]. Computer Methods in Applied Mechanics and Engineering. 1996,139: 3~47.
[8] Marcel, L. and Olivier, M. New Trends in Large-Eddy Simulations of Turbulence[J]. Annual Review of Fluid Mechanics. 1996, 28: 45~82.
[9] Moin, P. and Mahesh, K. Direct Numerical Simulation: A Tool in Turbulence Research[J]. Annual Review of Fluid Mechanics. 1998, 30: 539~578.
[10] Li, S.F. and Liu, W.K. Meshfree and Particle Methods and Their Applications[J]. Applied Mechanics Review. 2002, 55:1~34.
[11] Harlow, F.H. The Particle-In-Cell Computing Method for Fluid Dynamics[J]. Methods in Computational Physics. 1957, 3: 319~326.
[12] Harlow, F.H. and Welch, J. Numerical Calculation of Time-Dependent Viscous Incompressible Flow[J]. Physics of fluids. 1965, 8: 2182~2189.
[13] Nichols, D.B. and Hirt, C.W. SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free-Boundaries[R]. Los Alamos Scientific Laboratory, 1980, LA-8355.
[14] Osher, S. and Sethian, J.A. Fronts Propagation with Curvature Dependent Speed Algorithms Based on Hamilton-Jacobi Formulation[J]. Journal of Computer Physics, 1988, 79:12~49.
[15] Nayroles, B., Touzot, G. and Villon, P. Generalizing the Finite Element Method: Diffuse Approximation and Diffuse elements[J]. Computational Mechanics. 1992, 10: 307~318.
[16] Belytschko, T. Lu, Y.Y. and Gu, L. Element-Free Galerkin Methods[J]. International Journal for Numerical Method in Engineering. 1994, 37: 229~256.
[17]仇秩,由长福,祁海鹰,徐旭常.粘性不可压缩流畅数值模拟的无网格方法[J].清华大学学报(自然科学版). 2004, 44(2): 282~285.
[18]仇秩,由长福,祁海鹰,徐旭常.用无网格法求解不同Re下的圆柱绕流问题[J].清华大学学报(自然科学版). 2005, 45(2): 220~223.
[19] Liu, W. K. and Chen, Y.J. Wavelet and Multiple Scale Reproducing Kernel Methods. International Journal for Numerical Method in Fluids. 1995, 21: 901~931.
[20] Liu, W.K., Jun, S. and Zhang, Y.F. Reproducing Kernel Particle Methods[J]. International Journal for Numerical Method in Engineering. 1995, 20: 1081~1106.
[21] Liu, W.K., Chen, Y., Uras, R.A. and Chang, C.T. Generalized Multiple Scale Reproducing Kernel Particle[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 139: 91~157.
[22] Onarte, E.A. Finite Point Method in Computational Mechanics[J]. International Journal for Numerical Method in Engineering. 1996, 39: 3839~3866.
[23] Atluri, S.N. and Zhu, T.L. A New Meshless Local Petrov-Galerkin(MLPG) Approach in Computational Mechanics[J]. Computational Mechanics. 1998, 22:117~127.
[24] Atluri, S.N. and Kim, H.G. A Critical Assessment of the Truly Meshless Local Petrov-Galerkin(MLPG), and Local Boundary Integral Equation(LBIE) Methods[J]. Computational Mechanics.1999, 24: 348~372.
[25] Atluri, S.N. and Zhu, T.L. The Meshless Local Petrov-Galerkin(MLPG) Approach for Solving Problems in Elasto-Statics[J]. Computational Mechanics. 2000, 25:169~179.
[26] Atluri, S.N. and Zhu, T.L. New Concepts in Meshless Methods[J]. International Journal for Numerical Method in Engineering. 2000, 47: 537~556.
[27] Atluri, S.N. and Sladek, J. The Local Boundary Integral Equation(LBIE) and it’s Meshless Implementation for Linear Elasticity[J]. Computational Mechanics. 2000, 25: 180~198.
[28] Griebel M and Schweitzer M A Eds. Meshfree Methods for Partial Differential Equations [C]. Vol .1, Springer Verlag , 2000.
[29] Idelsohn, S.R., Onate, E., Calvo, N. and Del-Pin, F. The Meshless Finite Element Method[J]. International Journal for Numerical Method in Engineering. 2003, 58: 893~912.
[30] Hao, S., Park, H.S. and Liu, W.K. Moving Particle Finite Element Method[J]. International Journal for Numerical Method in Engineering. 2002, 53: 1937~1958.
[31] Zhu, T., Zhang, J.D. and Atluri, S.N. A Local Boundary Integral Equation(LBIE) Method inComputational Mechanics, and a Meshless Discretization Approach[J]. Computational Mechanics. 1998, 21: 223~235.
[32] Zhu, T., Zhang, J.D. and Atluri, S.N. A Meshless Local Boundary Integral Equation(LBIE) Method for Solving Nonlinear Problems[J]. Computational Mechanics. 1998, 22: 174~186.
[33] Zhu, T., Zhang, J.D. and Atluri, S.N. A Meshless Numerical Method Based on the Local Boundary Integral Equation(LBIE) to Solve Linear and Non-linear boundary Value Problems[J]. Engineering Analysis with Boundary Elements. 1999, 23: 375~389.
[34] Kothnur, V.S., Mukherjee,S. and Mukherjee, Y.X. Two Dimensional Linear Elasticity by the Boundary Node Method[J]. International Journal of Solids and Structures. 1999, 36: 1129~1147.
[35] Chati, M.K. Mukherjee, S. and Mukherjee, Y.X. The Boundary Node Method for Three-Dimensional Linear Elasticity[J] . International Journal for Numerical Mehod in Engineering. 1999, 46: 1163~1184.
[36] Batina, T.J. A Gridless Euler / Navier-Stokes Solution Algorithm for Complex Aircraft Applications[R]. AIAA Paper, 1993, 93~0333
[37] Morinishi, K. Efective Accuracy and Conservation Consistency of Gridless Type Solver[R]. Kyoto Institute of Technology, Kyoto, Japan, 1995,606~8585
[38] Duarte, C.A. and Oden, J.T. Hp Clouds-a Meshless Method to Solve Boundary-Value Problems[R]. Technical Report 95-05, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin. 1995.
[39] Liszka, T.J., Duarte, C.A.M. and Tworzydlo, W.W. hp-Meshless Cloud Method[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 139, 263~288.
[40] Oden, J.T., Duarte, C.A.M. and Zienkiewicz, O.C. A New Cloud-Based hp FEM[J]. Computer Methods in Applied Mechanics and Engineering. 1998, 153,117~126.
[41] Mendonca, P.de T.R., Barcellos, C.S. de and Duarte, A. Investigations on the hp-Cloud Method by Solving Timoshenko Beam Problems[J]. Computational Mechanics. 2000, 25: 286~295.
[42]陈全红.求解Euler方程的隐式无网格算法[J].计算物理. 2003, 20(1): 9~11.
[43]王刚,孙迎丹,叶正寅.无网格算法在多段翼型流动计算中的应用[J].应用力学学报. 2004, 21(3): 63~66.
[44]胡世祥,李磊,佘春东,唐智礼.二维Euler方程的无网格算法的精度分析[J].计算力学学报. 2005, 22(2): 232~236.
[45]江兴贤,陈红全.多段翼无网格算法及其布点研究[J].南京理工大学学报. 2005, 29(1): 22~25.
[46] Lucy, L.B. A Numerical Approach to the Testing of the Fission Hypothesis[J]. The Astron Journal. 1977, 8: 1013~1024.
[47] Mongahan, J. J. Shock Simulation by the Partiele Mehtod SPH[J]. Journal of Compute Physics. 1983, 52: 374~389.
[48] Monaghan, J.J. On the Problem of Penetration in Particle Methods[J]. Journal Computational Physics. 1989, 82: 1~15.
[49] Benz, W. Numerical Modeling of Nonlinear Stellar Pulsation: Problems and Prospects. Kluwer Academic, Boston, MA, 1990: 269.
[50] Petschek, A. G.., Libersky, L. D. Cylindral Smoothed Particle Hydrodynamics[J]. Journal of Computer Physics. 1993, 109: 76~83.
[51] Libersky, L. D., Petschek, A. G.. High Strain Lagrangian Hydrodynmaics-A Three Dimensionan SPH Code for Dynamics Material Response[J]. Journal of Computer Physics. 1993, 109: 67~75.
[52] Monaghan, J.J. Simulating Free Surface Flows with SPH[J]. Journal Computational Physics. 1994, 110: 399~406.
[53] Monaghan, J. J., Thompson, M. C., Hourigan, K. Simulation of Free Surface with SPH[J]. Porceedings of the l994 ASME Fluid Engineering Division Summer Meeting Partl8, 1994.
[54] Monaghan, J. J., Kocharyan, A. SPH Simulation of Multi-phase Flow[J]. Computer Physics Communications. 1995, 87:225~235.
[55] Johnson, G. R., Stryk, R. A., Beissel, S. R. SPH for High Velocity Impact Computation[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 20: 347~373.
[56] Hayhurst, C. J., Clegg, R. A. Cylindrical Symmetical SPH Simulations of Hypervelocity Impacts on Thin Plates[J]. Internatioanl Journal of Impact Engineering. 1997, 20: 337~348.
[57] Morris, J.P., Fox, P.J. and Shu, Y. Modeling Lower Reynolds Number Incompressible Flows Using SPH[J]. Journal Computational Physics. 1997, 136: 214~226.
[58] Reichl, P. J., Morris, P. J., Hourigan, K., Thompson, M. C., Stoneman, S. A. T. Free Surafee Flows Using Smoothed Partieles Hydordynmaics[J]. Proceedings of the 1997 ASME Fluid Engineering Division Summer Meeting Part18, 1997.
[59] Bonet, J. and Kulasegaram, S. Corrections and Stabilization of Smooth Particle Hydrodynamics Methods with Applications in Metal Forming Simulations[J]. International Journal for Numerical Methods In Engineering. 2000, 47: 1189~1214.
[60] Monaghan, J.J. SPH without Tensile Instability[J]. Journal Computational Physics. 2000, 159: 290~311.
[61] Edmond Y.M. L. and Shao, S.D. Simulation of Near-Shore Solitary Wave Mechanics by an Incompressible SPH Method[J]. Applied Ocean Research. 2002, 24: 275~286.
[62] Gómez-Gesteira, M., Cerqueiro, D., Crespo, C. and Dalrymple, R. Green Water Overtopping Analyzed with a SPH Model[J]. Ocean Engineering. 2005, 32: 223~238.
[63] Dalrymple, R.A. and Rogers, B.D. Numerical Modeling of Water Waves with the SPH Method[J]. Coastal Engineering. 2006, 53: 141~147.
[64] Shao, S.D. Incompressible SPH Simulation of Wave Breaking and Overtopping with Turbulence Modelling[J]. International Journal for Numerical Methods in Fluids. 2006, 50: 597~621.
[65] Shao, S.D. and Ji, C.M. SPH Computation of Plunging Waves Using a 2D Sub-Particle Scale(SPS) Turbulence Model[J]. International Journal for Numerical Methods in Fluids. 2006, 51: 913~936.
[66] Violeau, D. and Issa, R. Numerical Modelling of Complex Turbulent Free-Surface Flows with the SPH Method-The Overview[J]. International Journal for Numerical Methods in Fluids. 2007, 53: 277~304.
[67]贝新源,岳宗五.平滑粒子流体动力学[M].高科技研究中的数值计算(第一卷). 1995.
[68]张锁春.光滑粒子流体动力学(SPH)方法(综述)[J].计算物理. 1996, 13(4): 385~397.
[69]汤文辉,毛益明,岳宗五.光滑粒子流体动力学方法[J].高压物理学报. 1999 (增刊): 282
[70]董师舜,王邦荣.三维耦合光滑粒子动力学方法[J].爆炸与冲击. 1999(增刊): 188
[71]张刚明,王肖钧,胡秀章,周钟.光滑粒子法中的一种新的核函数[J].爆炸与冲击. 2003, 23(3): 219~224.
[72]宗智,邹丽,刘谋斌,王喜军.模拟二维水下爆炸问题的光滑粒子SPH方法[J].水动力学研究与进展. 2007, 22(1): 61~67.
[73] Koshizuka, S., Tamako, H. and Oka, Y. A Particle Method for Incompressible Viscous Flow with Fluid Fragmentation[J]. Journal of Computational Fluid Dynamics. 1995, 4: 29~46.
[74] Koshizuka, S. and Oka, Y. Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid[J]. Nuclear Science and Engineering. 1996, 123: 421~434.
[75] Koshizuka S., Ikeda, H. and Oka, Y. Numerical Analysis of Fragmentation Mechanisms in Vapor Explosions[J]. Nuclear Engineering and Design. 1999, 189: 426~433.
[76] Yoon, H.Y., Koshizuka, S. and Oka, Y. A Mesh-Free Numerical Method for Direct Simulation of Gas-Liquid Phase Interface[J]. Nuclear Science and Engineering. 1999, 133: 192~200.
[77] Yoon, H.Y., Koshizuka, S. and Oka, Y. A Particle-Gridless Hybrid Method for Incompressible Flows[J]. International Journal for Numerical Methods in Fluids. 1999, 30: 407~424.
[78] Gotoh, H. and Sakai, T. Largrangian Simulation of Breaking Waves Using Particle Method[J].Coast Engineering Journal. 1999, 41: 303~326.
[79] Chikazawa, Y., Koshizuka, S. and Oka, Y. A Particle Method for Elastic and Visco-Plastic Structures and Fuid-Structure Iteractions[J]. Computational Mechanics. 2001, 27: 97~106.
[80] Yoon, H.Y., Koshizuka, S. and Oka, Y. Direct Calculation of Bubble Growth, Departure, and Rise in Nucleate Pool Boiling[J]. International Journal of Multiphase. 2001, 27: 277~298.
[81]後藤仁志,酒井哲郎,芝原知树. SPS乱流モデリの導入による新しい罻臃à握归_[J].水工学論文集. 2000, 44: 575-579.
[82]後藤仁志,林焾,織田晃治,酒井哲郎. SPS乱流モデル付き拡張MPS法による砕波過程の数値解析[J].海岸工学論文集. 2002, 49: 31~35.
[83] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part1) [J]. Journal of Kansai Society Naval Architects. 2001, 236: 191~198. (in Japanese)
[84] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part2) [J]. Journal of Kansai Society Naval Architects. 2002, 237: 181~186. (in Japanese)
[85] Yoon, H.Y., Koshizuka, S. and Oka, Y. Numerical Analysis of Boiling on High Heat-Flux and High Subcooling Condition Using MPS-MAFL[J]. International Journal of Heat and Mass Transfer. 2002, 45: 2633~2642.
[86] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part3) [J]. Journal of Kansai Society Naval Architects. 2003, 239: 81~86. (in Japanese)
[87] Sueyoshi, M. Numerical Simulation of Extreme Motions of a Floating Body by MPS Method[J]. 2004, IEEE.
[88] Hibi, S. and Yabushita, K. A Study on Reduction of Unusual Pressure Fluctuation of MPS Method[J]. Journal of Kansai Society Naval Architects. 2004, 241: 125~131. (in Japanese)
[89] Guo, J. and Tao, Z. Modified Moving Particle Semi-Implicit Meshless Method for Incompressible Fluids[J]. Journal of Thermal Science. 2004, 13: 226~234.
[90] Xie, H., Koshizuka, S. and Oka, Y. Simulation of Drop Deposition Process in Annular Mist Flow Using Three-Dimensional Particle Method[J]. Nuclear Engineering and Design. 2005, 235: 1687~1697.
[91] Shao, S.D. and Gotoh, H. Turbulence Particle Models for Tracking Free Surfaces[J]. Journal of Hydraulic Research. 2005, 43: 276~289.
[92] Ataie-Ashtiani, B. and Farhadi, L. A Stable Moving-Particle Semi-Implicit Method for Free Surface Flows[J]. Fluid Dynamics. 2006, 38: 241~256.
[93] Wang, Q., Zheng, Y., Chen, C., Fujimoto, T. and Chiba, N. Efficient Rendering of Breaking WavesUsing MPS Method[J]. Journal of Zhejiang University Science A. 2006, 7:1018~1025.
[94] Gotoh, H. et al. Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall[J]. Coastal Engineering Journal, 2005, 47:157~181.
[95] Lee, C.J.K., Noguchi, H. and Koshizuka, S. Fluid-shell Structure Interaction Analysis by Coupled Particle and Finite Element Method[J]. Computers and Structures, 2007, 80:688–697.
[96] Ikejiri, S., Liu, J. and Oka, Y. Simulation of a Single Bubble Rising with Hybrid Particle-Mesh Method[J]. Journal of Nuclear Science and Technology, 2007, 44:886~893.
[97] Sueyoshi, M., Kihara, H. and Kashiwagi, M. Numerical Simulation of Deck Wetness for a 2D Pontoon-Type Floating Structure[J]. 2008, IEEE.
[98] Alam, A., Kai, H. and Suzuki, K. Two-Dimensional Numerical Simulation of Water Splash Phenomena With and Without Surface Tension[J]. Journal of Marine Science and Technology, 2007, 12:59~71.
[99] Suzuki, Y., Koshizuka, S. and Oka, Y. Hamiltonian Moving-Particle Semi-Implicit (HMPS) Method for Incompressible Fluid Flows[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196:2876~2894.
[100] Sueyoshi, M., Kashiwagi, M. and Naito, S. Numerical Simulation of Wave-Induced Nonlinear Motions of a Two-Dimensional Floating Body by the Moving Particle Semi-Implicit Method[J]. Journal of Marine Science and Technology, 2008, 13:85~94.
[101] Suzuki, Y. and Koshizuka, S. Numerical Simulation of Standing Waves Using the Hamiltonian Particle Method[J]. Journal of Japan Society of Mechanical Engineers. 2008, 74: 1018~1025. (in Japanese)
[102] Khayyer, A. and Gotoh, H. Development of CMPS Method for Accurate Water-Surface Tracing in Breaking Waves[J]. Coastal Engineering Journal, 2008, 50:179~207.
[103]郭隽,陶智.非线性问题的MPS无网格算法[J].北京航空航天大学学报. 2003, 29(1): 83~86.
[104]李邵武,尹振军.无网格数值方法在结构物水动力研究中的应用[J].水科学进展. 2004, 15(6): 739~744.
[105]段日强,姜胜耀,张佑杰,贾海军,杨星团.二维数值模拟蒸汽膜覆盖的液滴水力学特性[J].中国科学E. 2005, 35(3): 314~323.
[106]段日强,姜胜耀,张佑杰,贾海军,杨星团.用无网格粒子法直接模拟多相多组分界面流[J].清华大学学报(自然科学版). 2005, 45(6): 835~838.
[107]段日强,姜胜耀,张佑杰,贾海军,杨星团.采用无网格移动粒子法数值模拟闪蒸射流[J].原子能科学技术. 2006, 40(1): 61~66.
[108]席光,项利峰.自由表面流动的移动粒子半隐式模拟方法[J].西安交通大学学报. 2006, 40(3): 249~252,288.
[109]李邵武,熊赞,武霄. MPS水流数学模型在冲击压力计算中的应用[J].天津大学学报. 2006, 39(9): 1031~1036.
[110]孙中国,席光,项利峰.基于无网格法的水中气泡上升运动数值模拟[J].工程热物理学报. 2007, 28(5): 772~774.
[111]孙中国,席光,项利峰.不可压缩流动的移动粒子半隐式法数值模拟[J].应用力学学报. 2007, 24(3): 440~442.
[112]徐刚,段文洋.自由面流动模拟的MPS算法研究[J].哈尔滨工程大学学报. 2008, 29(3): 539~543.
[113] Ikeda, Y., Komatsu, K., Himeno, Y. and Tanaka, N. On Roll Damping Force of Ship[J]. Journal of Kansai Society Naval Architects. 1977, 165: 31~39. (in Japanese)
[114] Ikeda, Y., Himeno, Y. and Tanaka, N. On Eddy Making Component of Roll Damping Force on Naked Hull[J]. Journal of Society Naval Architects of Japan. 1977, 142:54~64. (in Japanese)
[115] Ikeda, Y., Himeno, Y. and Tanaka, N. Components of Roll Damping of Ship at Forward Speed[J]. Journal of Society Naval Architects of Japan. 1978, 143:113~125. (in Japanese)
[116] Ikeda, Y., Himeno, Y. and Tanaka, N. Prediction Method for Ship Roll Damping[R]. No.00405 of Department of Naval Architecture, University of Osaka Prefecture, 1978.
[117] Zhang, H.X., Liu, Y.Z., and Miao, G.P. Vertex Patterns and Roll Damping on Various Cross Sections of Ship[J]. China Ocean Engineering, 2000, 14:185~192.
[118] Chakrabarti, S. Empirical calculation of roll damping for ships and barges[J]. Ocean Engineering Journal, 2001, 28:915~932.
[119]张怀新,缪国平,刘应中,朱天宇.三维振荡船体贴体网格的生成[J].上海交通大学学报. 1996, 30(10): 28~34.
[120]张怀新,朱天宇,缪国平,刘应中.摇荡物体周围粘性流的数值模拟[J].上海交通大学学报. 1997, 31(11): 121~126.
[121]张怀新,刘应中,缪国平.船体各种剖面的横摇阻尼与漩涡的形状[J].水动力学研究与进展. 2001, 16(3): 382~389.
[122]张怀新,刘应中,缪国平.带自由表面三维船体周围粘性流场的数值模拟[J].上海交通大学学报. 2001, 35(10): 1429~1432.
[123]潘雨村,张怀新.用密度函数法对自由表面进行数值模拟[J].水动力学研究与进展. 2004, 19(6): 726~732.
[124] Amsden, A.A. and Harlow. F.H. A Simplified MAC technique for Incompressible Fluid Calculations[J]. Journal of Computer Physics, 1970, 6:322~325.
[125] Vievelli, J.A. A Computing Method for Incompressible Flows Bounded by Moving Walls[J]. Journal of Computer Physics, 1971, 8:119~143.
[126] Chan, K.C. and Stree, R.L. A Computer Study of Finite Amplitude Water Wave[J]. Journal of Computer Physics, 1970, 6:68~94.
[127] Hino, T., Miyata, H. and Kajitani, H. A Numerical Method for Nonlinear Shallow Water Waver[J]. Journal of Society Naval Architects of Japan. 1983, 153:1~12. (in Japanese)
[128] Hirt, C.W. and Nicholos, B.D. Volume of Fluid (VOF) Method for Dynamics of Free Boundaries[J]. Journal of Computer Physics, 1981, 39:201~225.
[129] Prandtl, L. and Uber, D.A. Turbulenz. ZAMM[M]. 1925,5:136.
[130]Taylor, G.I. Statistical Theory of Turbulence[R]. Parts 1-4, Proc. of Royal Soc. of London, Series A.1935,151:421.
[131] Kolmogorov, A.N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers[R]. C.R.Acad.Sci., U.R.S.S..1941,30:301.
[132] Rodi, W. Turbulence Models and Their Application in Hydraulics[R]. IAHR-monograph, Delft.1980.
[133] Bedford, K., Findikakis, A., Larock, B.E., Rodi, W. and Street, R.L. Turbulence Modeling of Surface Water Flow and Transport[J]. Journal of Hydraulic Engineering, ASCE, 1988,114: 969~1073.
[134] Deardorff, J.W. A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Number[J]. Journal of Fluid Mechanics.1970, 41:453~480.
[135] Schumann, U. Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Amuli[J]. Journal of Computer Physics, 1975, 18:376~404.
[136] Smagorinsky, J. General Circulation Experiments with the Primitive Equations[J]. Monthly Weather Review, 1963, 91:99~164.
[137] Bardina, J. and Ferziger, J.H. Reynolds W C. Improved Subgrid Scale Models for Large Eddy Simulation[J]. AIAA, 1980:80~1357.
[138] Schumann, U. Doctoral Dissertation, Technical Univ. of Karlsruhe, Germany. Also KFK-Bericht 1854, Kemforschungszentrum Karlsruhe, 1973
[139] Moin, P. and Kim, J. Numerical Investigation of Turbulent Channel Flow[J]. Journal of Fluid Mechanics, 1982, 118:341~377.
[140] Kim, J., Moin, P. and Moser, R.D. Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number[J]. Journal of Fluid Mechanics, 1987, 177:133~166.
[141] Lilly, D.K. On the Application of the Eddy Viscosity Concept in the Inertial Subrange of Turbulence[R]. NCAR Manuscript No. 123, National Center for Atmospheric Research, Boulder, Colorado ,1966
[142] Germano, M. et al. A Dynamic Subgrid-Scale Eddy Viscosity Model[J]. Journal of Physics Fluids A, 1991, 3:1760~1765.
[143] Lilly, D.K. A Proposed Modification of the Germano Subgrid-Scale Closure Method[J]. Journal of Physics Fluids A, 1992, 4:633~635.
[144] Clark, R.A., Ferziger, J.H. and Reynolds, W.C. Evaluation of Subgrid-Scale Models Using an Accurately Simulated Turbulent Flow[J]. Journal of Mechanics. 1979, 91:1~16.
[145] McMillan, O.J. and Feriziger, J.H. Direct Testing of Subgrid-Scale Models[J]. AIAA 1979, 17: 1340~1346.
[146] Lesieur, M. and Metais, O. New Trends in Large-Eddy Simulations of Turbulence[J]. Annual Reviews, 1996, 28:45~82.
[147] Meneveau, C. and Katz, J. Scale-Invariance and Turbulence Models for Large-Eddy Simulation[J]. Annual Reviewing Fluid Mechanics, 2000, 32:1~32.
[148] Li, C.W. and Wang, J.H. Large Eddy Simulation of Free Surface Shallow-Water Flow[J]. International Journal for Numerical Method in Fluid, 2000, 34:31~46.
[149] Piomelli, U. and Balaras, E. Wall-Layer Models for Large-Eddy Simulation[J]. Annual Reviewing Fluid Mechanics, 2002, 34:349~374.
[150] Pitsch, H. Large-Eddy Simulation of Turbulent Combustion[J]. Annual Reviewing Fluid Mechanics, 2006, 38:453~482.
[151] You, D., Wang, M. and Moin, P. Large-Eddy Simulation of Flow Over a Wall-Mounted Hump with Separation Control[J]. AIAA, 2006, 44:2571~2577.
[152] Jouhaud, J.C., Gicquel, L.Y.M. and Enaux, B. Large-Eddy-Simulation Modeling for Aerothermal Predictions Behind a Jet in Crossflow[J]. AIAA, 2007, 45:2438~2447.
[153] Razafindralandy, D., Hamdouni, A. and Oberlack, M. Analysis and Development of Subgrid Turbulence Models Preserving the Symmetry Properties of the Navier–Stokes Equations[J]. European Journal of Mechanics B/Fluids, 2007, 26:531~550.
[154] Lam, K. and Lin, Y.F. Large Eddy Simulation of Flow Around Wavy Cylinders at a Subcritical Reynolds Number[J]. International Journal of Heat and Fluid Flow, 2008, 29: 1071~1088.
[155]戴正元.大涡模拟滤波网格尺度研究及其应用[D].上海,上海交通大学, 2007.
[156]朱仁庆.液体晃荡及其与结构的相互作用[D].无锡,中国船舶科学研究中心, 2001.
[157] Graham, E.W. and Rodriguez, A.M. The Characteristics of Fuel Motion Which Affect Airplane Dynamics[J]. Journal of Applied Mechanics, 1952, 19:381~388.
[158] Housner, G. Dynamic Pressure on Accelerated Fluid Containers[J]. Bulletin of the Seismological Society of America, 1957, 47:15~35.
[159] Abramson, H.N. The Dynamic Behavior of Liquid in Moving Containers[R]. NASA SP-106, 1966.
[160] Nakayama, T. and Washizu, K. The Boundary Element Method Applied to The Analysis of Two-Dimensional Nonlinear Sloshing Problems[J]. International Journal for Numerical Methods in Engineering, 1981, 17:1631~1646.
[161] Mikelis, N.E. and Journee, J.M. Experimental and Numerical Simulations of Sloshing Behavior in Liquid Tanks and its Effect on Ship Motion[R]. National Conference on Numerical Methods for Transient and Coupled Problem, Venice, Italy, 1984.
[162] Hwang, J.H., Kim, I.S., Seol, Y.S. and Lee, S.C. Numerical Simulation of Liquid Sloshing in 3-Dimensional Tanks[J]. Journal of Computers and Structures, 1992, 44:339~342.
[163] Armenio, V. and Rocca, L.M. On the Analysis of Sloshing of Water in Rectangular Containers: Numerical Study and Experimental Validation[J]. Ocean Engeering, 1996, 23:705~739.
[164] Chen, W., Haroun, M.A. and Liu, F. Large Amplitude Liquid Sloshing in Seismically Excited Tank[J]. Earthquake Engeering and Stractural Dynamics, 1996, 25:653~669.
[165] Carious, A. nd Casella, G. Liquid Sloshing in Ship Tanks: a Comparative Study of Numerical Simulation[J]. Marine Structures, 1999, 12:183~198.
[166] Nielsen, K.B. Numerical Prediction of Green Water Loads on Ship[D]. Technical University of Denmark, Denmark, 2003.
[167] Yu, K. Level-Set RANS Method for Sloshing and Green Water Simulations[D]. Texas A&M University, Texas, 2007.
[168] Delorme, L. et al. A Set of Canonical Problems in Sloshing, Part I Pressure Field in Forced Roll Comparison Between Experimental Results and SPH[J]. Ocean Engineering, 2009, 36:168~178.
[169] Olsen, H. and Johnsen, K.R. Nonlinear Sloshing in Rectangular Tanks. A Pilot Study on The Applicability of Analytical Models[R]. Det Norske Veritas Report 74-72-S, vol. II, 1975.
[170] Lohner, R., Yang, C. and Onate, E. Simulation of Flows with Violent Free Surface Motion and Moving Objects Using Unstructured Grids[J]. International Journal for Numerical Methods inFluids, 2007, 53:1315~1338.
[171] Landrini, M., Colagorossi, A. and Faltisen, O.M. Sloshing in 2-D Flows by The SPH Method[J]. Proceedings of the 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea, 2003.
[172] Bass, R. et al. Modeling Criteria for Scaled LNG Sloshing Experiments[J]. Transactions of the ASME, 1985, 107:272~280.
[173] Peregrine, D. Water-Wave Impact on Walls[J]. Annual Review of Fluid Mechanics, 2003: 35: 23~43.
[174] Lee, Y.B. et al. An Experimental Study of Impulsive Sloshing Load Acting on LNG Tank[J]. Proceedings of the 16th ISOPE, 2006.
[175] Akyildrz, H. and Unal, N.E. Sloshing in a Three-Dimensional Rectangular Tank Numerical Simulation and Experimental Validation[J]. Ocean Engineering, 2006, 33:2135~2149.
[176] Lee, D.H. et al. A Parametric Sensitivity Study on LNG Tank Sloshing Loads by Numerical Simulations[J]. Ocean Engineering, 2007, 34:3~9.
[177] Faltisen, O.M. and Timokha, A.N. An Adaptive Multimodal Approach to Nonlinear Sloshing in a Rectangular Tank[J]. Journal of Fluid Mechanics, 2001, 432:167~200.
[178] Faltisen, O.M. and Timokha, A.N. Asymptotic Modal Approximation of Nonlinear Resonant Sloshing in a Rectangular Tank with Small Fluid Depth[J]. Journal of Fluid Mechanics, 2002, 470:319~357.
[179] Faltisen, O.M., Rognebakke, O.F. and Timokha, A.N. Resonant Three-Dimensional Nonlinear Sloshing in a Square-Base Basin[J]. Journal of Fluid Mechanics, 2003, 487:1~42.
[180] Faltisen, O.M., Rognebakke, O.F. and Timokha, A.N. Classification of Three-Dimensional Nonlinear Sloshing in a Square-Base Tank with Finite Depth[J]. Journal of Fluids and Structures, 2005, 20:81~103.
[2]张雄,宋康祖,陆明万.无网格法研究进展及其应用[J].计算力学学报. 2003, 20(6): 730~742.
[3]贾高顺,王晓光,梁利华,马修彦.无网格方法的应用前景[J].科技通报. 2003, 19(5): 360~364.
[4]李邵武,尹振军. N-S方程的数值解法及其在水波动力学中应用的综述[J].海洋通报. 2004, 23(4): 79~85.
[5]顾元通,丁桦.无网格法及其最新进展[J].力学进展. 2005, 35(3): 323~337.
[6]李九红,程玉明.无网格方法的研究进展与展望[J].力学季刊. 2006, 27(1): 143~152.
[7] Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. Meshless Method: An Overview and Recent Developments[J]. Computer Methods in Applied Mechanics and Engineering. 1996,139: 3~47.
[8] Marcel, L. and Olivier, M. New Trends in Large-Eddy Simulations of Turbulence[J]. Annual Review of Fluid Mechanics. 1996, 28: 45~82.
[9] Moin, P. and Mahesh, K. Direct Numerical Simulation: A Tool in Turbulence Research[J]. Annual Review of Fluid Mechanics. 1998, 30: 539~578.
[10] Li, S.F. and Liu, W.K. Meshfree and Particle Methods and Their Applications[J]. Applied Mechanics Review. 2002, 55:1~34.
[11] Harlow, F.H. The Particle-In-Cell Computing Method for Fluid Dynamics[J]. Methods in Computational Physics. 1957, 3: 319~326.
[12] Harlow, F.H. and Welch, J. Numerical Calculation of Time-Dependent Viscous Incompressible Flow[J]. Physics of fluids. 1965, 8: 2182~2189.
[13] Nichols, D.B. and Hirt, C.W. SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free-Boundaries[R]. Los Alamos Scientific Laboratory, 1980, LA-8355.
[14] Osher, S. and Sethian, J.A. Fronts Propagation with Curvature Dependent Speed Algorithms Based on Hamilton-Jacobi Formulation[J]. Journal of Computer Physics, 1988, 79:12~49.
[15] Nayroles, B., Touzot, G. and Villon, P. Generalizing the Finite Element Method: Diffuse Approximation and Diffuse elements[J]. Computational Mechanics. 1992, 10: 307~318.
[16] Belytschko, T. Lu, Y.Y. and Gu, L. Element-Free Galerkin Methods[J]. International Journal for Numerical Method in Engineering. 1994, 37: 229~256.
[17]仇秩,由长福,祁海鹰,徐旭常.粘性不可压缩流畅数值模拟的无网格方法[J].清华大学学报(自然科学版). 2004, 44(2): 282~285.
[18]仇秩,由长福,祁海鹰,徐旭常.用无网格法求解不同Re下的圆柱绕流问题[J].清华大学学报(自然科学版). 2005, 45(2): 220~223.
[19] Liu, W. K. and Chen, Y.J. Wavelet and Multiple Scale Reproducing Kernel Methods. International Journal for Numerical Method in Fluids. 1995, 21: 901~931.
[20] Liu, W.K., Jun, S. and Zhang, Y.F. Reproducing Kernel Particle Methods[J]. International Journal for Numerical Method in Engineering. 1995, 20: 1081~1106.
[21] Liu, W.K., Chen, Y., Uras, R.A. and Chang, C.T. Generalized Multiple Scale Reproducing Kernel Particle[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 139: 91~157.
[22] Onarte, E.A. Finite Point Method in Computational Mechanics[J]. International Journal for Numerical Method in Engineering. 1996, 39: 3839~3866.
[23] Atluri, S.N. and Zhu, T.L. A New Meshless Local Petrov-Galerkin(MLPG) Approach in Computational Mechanics[J]. Computational Mechanics. 1998, 22:117~127.
[24] Atluri, S.N. and Kim, H.G. A Critical Assessment of the Truly Meshless Local Petrov-Galerkin(MLPG), and Local Boundary Integral Equation(LBIE) Methods[J]. Computational Mechanics.1999, 24: 348~372.
[25] Atluri, S.N. and Zhu, T.L. The Meshless Local Petrov-Galerkin(MLPG) Approach for Solving Problems in Elasto-Statics[J]. Computational Mechanics. 2000, 25:169~179.
[26] Atluri, S.N. and Zhu, T.L. New Concepts in Meshless Methods[J]. International Journal for Numerical Method in Engineering. 2000, 47: 537~556.
[27] Atluri, S.N. and Sladek, J. The Local Boundary Integral Equation(LBIE) and it’s Meshless Implementation for Linear Elasticity[J]. Computational Mechanics. 2000, 25: 180~198.
[28] Griebel M and Schweitzer M A Eds. Meshfree Methods for Partial Differential Equations [C]. Vol .1, Springer Verlag , 2000.
[29] Idelsohn, S.R., Onate, E., Calvo, N. and Del-Pin, F. The Meshless Finite Element Method[J]. International Journal for Numerical Method in Engineering. 2003, 58: 893~912.
[30] Hao, S., Park, H.S. and Liu, W.K. Moving Particle Finite Element Method[J]. International Journal for Numerical Method in Engineering. 2002, 53: 1937~1958.
[31] Zhu, T., Zhang, J.D. and Atluri, S.N. A Local Boundary Integral Equation(LBIE) Method inComputational Mechanics, and a Meshless Discretization Approach[J]. Computational Mechanics. 1998, 21: 223~235.
[32] Zhu, T., Zhang, J.D. and Atluri, S.N. A Meshless Local Boundary Integral Equation(LBIE) Method for Solving Nonlinear Problems[J]. Computational Mechanics. 1998, 22: 174~186.
[33] Zhu, T., Zhang, J.D. and Atluri, S.N. A Meshless Numerical Method Based on the Local Boundary Integral Equation(LBIE) to Solve Linear and Non-linear boundary Value Problems[J]. Engineering Analysis with Boundary Elements. 1999, 23: 375~389.
[34] Kothnur, V.S., Mukherjee,S. and Mukherjee, Y.X. Two Dimensional Linear Elasticity by the Boundary Node Method[J]. International Journal of Solids and Structures. 1999, 36: 1129~1147.
[35] Chati, M.K. Mukherjee, S. and Mukherjee, Y.X. The Boundary Node Method for Three-Dimensional Linear Elasticity[J] . International Journal for Numerical Mehod in Engineering. 1999, 46: 1163~1184.
[36] Batina, T.J. A Gridless Euler / Navier-Stokes Solution Algorithm for Complex Aircraft Applications[R]. AIAA Paper, 1993, 93~0333
[37] Morinishi, K. Efective Accuracy and Conservation Consistency of Gridless Type Solver[R]. Kyoto Institute of Technology, Kyoto, Japan, 1995,606~8585
[38] Duarte, C.A. and Oden, J.T. Hp Clouds-a Meshless Method to Solve Boundary-Value Problems[R]. Technical Report 95-05, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin. 1995.
[39] Liszka, T.J., Duarte, C.A.M. and Tworzydlo, W.W. hp-Meshless Cloud Method[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 139, 263~288.
[40] Oden, J.T., Duarte, C.A.M. and Zienkiewicz, O.C. A New Cloud-Based hp FEM[J]. Computer Methods in Applied Mechanics and Engineering. 1998, 153,117~126.
[41] Mendonca, P.de T.R., Barcellos, C.S. de and Duarte, A. Investigations on the hp-Cloud Method by Solving Timoshenko Beam Problems[J]. Computational Mechanics. 2000, 25: 286~295.
[42]陈全红.求解Euler方程的隐式无网格算法[J].计算物理. 2003, 20(1): 9~11.
[43]王刚,孙迎丹,叶正寅.无网格算法在多段翼型流动计算中的应用[J].应用力学学报. 2004, 21(3): 63~66.
[44]胡世祥,李磊,佘春东,唐智礼.二维Euler方程的无网格算法的精度分析[J].计算力学学报. 2005, 22(2): 232~236.
[45]江兴贤,陈红全.多段翼无网格算法及其布点研究[J].南京理工大学学报. 2005, 29(1): 22~25.
[46] Lucy, L.B. A Numerical Approach to the Testing of the Fission Hypothesis[J]. The Astron Journal. 1977, 8: 1013~1024.
[47] Mongahan, J. J. Shock Simulation by the Partiele Mehtod SPH[J]. Journal of Compute Physics. 1983, 52: 374~389.
[48] Monaghan, J.J. On the Problem of Penetration in Particle Methods[J]. Journal Computational Physics. 1989, 82: 1~15.
[49] Benz, W. Numerical Modeling of Nonlinear Stellar Pulsation: Problems and Prospects. Kluwer Academic, Boston, MA, 1990: 269.
[50] Petschek, A. G.., Libersky, L. D. Cylindral Smoothed Particle Hydrodynamics[J]. Journal of Computer Physics. 1993, 109: 76~83.
[51] Libersky, L. D., Petschek, A. G.. High Strain Lagrangian Hydrodynmaics-A Three Dimensionan SPH Code for Dynamics Material Response[J]. Journal of Computer Physics. 1993, 109: 67~75.
[52] Monaghan, J.J. Simulating Free Surface Flows with SPH[J]. Journal Computational Physics. 1994, 110: 399~406.
[53] Monaghan, J. J., Thompson, M. C., Hourigan, K. Simulation of Free Surface with SPH[J]. Porceedings of the l994 ASME Fluid Engineering Division Summer Meeting Partl8, 1994.
[54] Monaghan, J. J., Kocharyan, A. SPH Simulation of Multi-phase Flow[J]. Computer Physics Communications. 1995, 87:225~235.
[55] Johnson, G. R., Stryk, R. A., Beissel, S. R. SPH for High Velocity Impact Computation[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 20: 347~373.
[56] Hayhurst, C. J., Clegg, R. A. Cylindrical Symmetical SPH Simulations of Hypervelocity Impacts on Thin Plates[J]. Internatioanl Journal of Impact Engineering. 1997, 20: 337~348.
[57] Morris, J.P., Fox, P.J. and Shu, Y. Modeling Lower Reynolds Number Incompressible Flows Using SPH[J]. Journal Computational Physics. 1997, 136: 214~226.
[58] Reichl, P. J., Morris, P. J., Hourigan, K., Thompson, M. C., Stoneman, S. A. T. Free Surafee Flows Using Smoothed Partieles Hydordynmaics[J]. Proceedings of the 1997 ASME Fluid Engineering Division Summer Meeting Part18, 1997.
[59] Bonet, J. and Kulasegaram, S. Corrections and Stabilization of Smooth Particle Hydrodynamics Methods with Applications in Metal Forming Simulations[J]. International Journal for Numerical Methods In Engineering. 2000, 47: 1189~1214.
[60] Monaghan, J.J. SPH without Tensile Instability[J]. Journal Computational Physics. 2000, 159: 290~311.
[61] Edmond Y.M. L. and Shao, S.D. Simulation of Near-Shore Solitary Wave Mechanics by an Incompressible SPH Method[J]. Applied Ocean Research. 2002, 24: 275~286.
[62] Gómez-Gesteira, M., Cerqueiro, D., Crespo, C. and Dalrymple, R. Green Water Overtopping Analyzed with a SPH Model[J]. Ocean Engineering. 2005, 32: 223~238.
[63] Dalrymple, R.A. and Rogers, B.D. Numerical Modeling of Water Waves with the SPH Method[J]. Coastal Engineering. 2006, 53: 141~147.
[64] Shao, S.D. Incompressible SPH Simulation of Wave Breaking and Overtopping with Turbulence Modelling[J]. International Journal for Numerical Methods in Fluids. 2006, 50: 597~621.
[65] Shao, S.D. and Ji, C.M. SPH Computation of Plunging Waves Using a 2D Sub-Particle Scale(SPS) Turbulence Model[J]. International Journal for Numerical Methods in Fluids. 2006, 51: 913~936.
[66] Violeau, D. and Issa, R. Numerical Modelling of Complex Turbulent Free-Surface Flows with the SPH Method-The Overview[J]. International Journal for Numerical Methods in Fluids. 2007, 53: 277~304.
[67]贝新源,岳宗五.平滑粒子流体动力学[M].高科技研究中的数值计算(第一卷). 1995.
[68]张锁春.光滑粒子流体动力学(SPH)方法(综述)[J].计算物理. 1996, 13(4): 385~397.
[69]汤文辉,毛益明,岳宗五.光滑粒子流体动力学方法[J].高压物理学报. 1999 (增刊): 282
[70]董师舜,王邦荣.三维耦合光滑粒子动力学方法[J].爆炸与冲击. 1999(增刊): 188
[71]张刚明,王肖钧,胡秀章,周钟.光滑粒子法中的一种新的核函数[J].爆炸与冲击. 2003, 23(3): 219~224.
[72]宗智,邹丽,刘谋斌,王喜军.模拟二维水下爆炸问题的光滑粒子SPH方法[J].水动力学研究与进展. 2007, 22(1): 61~67.
[73] Koshizuka, S., Tamako, H. and Oka, Y. A Particle Method for Incompressible Viscous Flow with Fluid Fragmentation[J]. Journal of Computational Fluid Dynamics. 1995, 4: 29~46.
[74] Koshizuka, S. and Oka, Y. Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid[J]. Nuclear Science and Engineering. 1996, 123: 421~434.
[75] Koshizuka S., Ikeda, H. and Oka, Y. Numerical Analysis of Fragmentation Mechanisms in Vapor Explosions[J]. Nuclear Engineering and Design. 1999, 189: 426~433.
[76] Yoon, H.Y., Koshizuka, S. and Oka, Y. A Mesh-Free Numerical Method for Direct Simulation of Gas-Liquid Phase Interface[J]. Nuclear Science and Engineering. 1999, 133: 192~200.
[77] Yoon, H.Y., Koshizuka, S. and Oka, Y. A Particle-Gridless Hybrid Method for Incompressible Flows[J]. International Journal for Numerical Methods in Fluids. 1999, 30: 407~424.
[78] Gotoh, H. and Sakai, T. Largrangian Simulation of Breaking Waves Using Particle Method[J].Coast Engineering Journal. 1999, 41: 303~326.
[79] Chikazawa, Y., Koshizuka, S. and Oka, Y. A Particle Method for Elastic and Visco-Plastic Structures and Fuid-Structure Iteractions[J]. Computational Mechanics. 2001, 27: 97~106.
[80] Yoon, H.Y., Koshizuka, S. and Oka, Y. Direct Calculation of Bubble Growth, Departure, and Rise in Nucleate Pool Boiling[J]. International Journal of Multiphase. 2001, 27: 277~298.
[81]後藤仁志,酒井哲郎,芝原知树. SPS乱流モデリの導入による新しい罻臃à握归_[J].水工学論文集. 2000, 44: 575-579.
[82]後藤仁志,林焾,織田晃治,酒井哲郎. SPS乱流モデル付き拡張MPS法による砕波過程の数値解析[J].海岸工学論文集. 2002, 49: 31~35.
[83] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part1) [J]. Journal of Kansai Society Naval Architects. 2001, 236: 191~198. (in Japanese)
[84] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part2) [J]. Journal of Kansai Society Naval Architects. 2002, 237: 181~186. (in Japanese)
[85] Yoon, H.Y., Koshizuka, S. and Oka, Y. Numerical Analysis of Boiling on High Heat-Flux and High Subcooling Condition Using MPS-MAFL[J]. International Journal of Heat and Mass Transfer. 2002, 45: 2633~2642.
[86] Sueyoshi, M. and Naito, S. A Study of Nonlinear Fluid Phenomena with Particle Method (Part3) [J]. Journal of Kansai Society Naval Architects. 2003, 239: 81~86. (in Japanese)
[87] Sueyoshi, M. Numerical Simulation of Extreme Motions of a Floating Body by MPS Method[J]. 2004, IEEE.
[88] Hibi, S. and Yabushita, K. A Study on Reduction of Unusual Pressure Fluctuation of MPS Method[J]. Journal of Kansai Society Naval Architects. 2004, 241: 125~131. (in Japanese)
[89] Guo, J. and Tao, Z. Modified Moving Particle Semi-Implicit Meshless Method for Incompressible Fluids[J]. Journal of Thermal Science. 2004, 13: 226~234.
[90] Xie, H., Koshizuka, S. and Oka, Y. Simulation of Drop Deposition Process in Annular Mist Flow Using Three-Dimensional Particle Method[J]. Nuclear Engineering and Design. 2005, 235: 1687~1697.
[91] Shao, S.D. and Gotoh, H. Turbulence Particle Models for Tracking Free Surfaces[J]. Journal of Hydraulic Research. 2005, 43: 276~289.
[92] Ataie-Ashtiani, B. and Farhadi, L. A Stable Moving-Particle Semi-Implicit Method for Free Surface Flows[J]. Fluid Dynamics. 2006, 38: 241~256.
[93] Wang, Q., Zheng, Y., Chen, C., Fujimoto, T. and Chiba, N. Efficient Rendering of Breaking WavesUsing MPS Method[J]. Journal of Zhejiang University Science A. 2006, 7:1018~1025.
[94] Gotoh, H. et al. Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall[J]. Coastal Engineering Journal, 2005, 47:157~181.
[95] Lee, C.J.K., Noguchi, H. and Koshizuka, S. Fluid-shell Structure Interaction Analysis by Coupled Particle and Finite Element Method[J]. Computers and Structures, 2007, 80:688–697.
[96] Ikejiri, S., Liu, J. and Oka, Y. Simulation of a Single Bubble Rising with Hybrid Particle-Mesh Method[J]. Journal of Nuclear Science and Technology, 2007, 44:886~893.
[97] Sueyoshi, M., Kihara, H. and Kashiwagi, M. Numerical Simulation of Deck Wetness for a 2D Pontoon-Type Floating Structure[J]. 2008, IEEE.
[98] Alam, A., Kai, H. and Suzuki, K. Two-Dimensional Numerical Simulation of Water Splash Phenomena With and Without Surface Tension[J]. Journal of Marine Science and Technology, 2007, 12:59~71.
[99] Suzuki, Y., Koshizuka, S. and Oka, Y. Hamiltonian Moving-Particle Semi-Implicit (HMPS) Method for Incompressible Fluid Flows[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196:2876~2894.
[100] Sueyoshi, M., Kashiwagi, M. and Naito, S. Numerical Simulation of Wave-Induced Nonlinear Motions of a Two-Dimensional Floating Body by the Moving Particle Semi-Implicit Method[J]. Journal of Marine Science and Technology, 2008, 13:85~94.
[101] Suzuki, Y. and Koshizuka, S. Numerical Simulation of Standing Waves Using the Hamiltonian Particle Method[J]. Journal of Japan Society of Mechanical Engineers. 2008, 74: 1018~1025. (in Japanese)
[102] Khayyer, A. and Gotoh, H. Development of CMPS Method for Accurate Water-Surface Tracing in Breaking Waves[J]. Coastal Engineering Journal, 2008, 50:179~207.
[103]郭隽,陶智.非线性问题的MPS无网格算法[J].北京航空航天大学学报. 2003, 29(1): 83~86.
[104]李邵武,尹振军.无网格数值方法在结构物水动力研究中的应用[J].水科学进展. 2004, 15(6): 739~744.
[105]段日强,姜胜耀,张佑杰,贾海军,杨星团.二维数值模拟蒸汽膜覆盖的液滴水力学特性[J].中国科学E. 2005, 35(3): 314~323.
[106]段日强,姜胜耀,张佑杰,贾海军,杨星团.用无网格粒子法直接模拟多相多组分界面流[J].清华大学学报(自然科学版). 2005, 45(6): 835~838.
[107]段日强,姜胜耀,张佑杰,贾海军,杨星团.采用无网格移动粒子法数值模拟闪蒸射流[J].原子能科学技术. 2006, 40(1): 61~66.
[108]席光,项利峰.自由表面流动的移动粒子半隐式模拟方法[J].西安交通大学学报. 2006, 40(3): 249~252,288.
[109]李邵武,熊赞,武霄. MPS水流数学模型在冲击压力计算中的应用[J].天津大学学报. 2006, 39(9): 1031~1036.
[110]孙中国,席光,项利峰.基于无网格法的水中气泡上升运动数值模拟[J].工程热物理学报. 2007, 28(5): 772~774.
[111]孙中国,席光,项利峰.不可压缩流动的移动粒子半隐式法数值模拟[J].应用力学学报. 2007, 24(3): 440~442.
[112]徐刚,段文洋.自由面流动模拟的MPS算法研究[J].哈尔滨工程大学学报. 2008, 29(3): 539~543.
[113] Ikeda, Y., Komatsu, K., Himeno, Y. and Tanaka, N. On Roll Damping Force of Ship[J]. Journal of Kansai Society Naval Architects. 1977, 165: 31~39. (in Japanese)
[114] Ikeda, Y., Himeno, Y. and Tanaka, N. On Eddy Making Component of Roll Damping Force on Naked Hull[J]. Journal of Society Naval Architects of Japan. 1977, 142:54~64. (in Japanese)
[115] Ikeda, Y., Himeno, Y. and Tanaka, N. Components of Roll Damping of Ship at Forward Speed[J]. Journal of Society Naval Architects of Japan. 1978, 143:113~125. (in Japanese)
[116] Ikeda, Y., Himeno, Y. and Tanaka, N. Prediction Method for Ship Roll Damping[R]. No.00405 of Department of Naval Architecture, University of Osaka Prefecture, 1978.
[117] Zhang, H.X., Liu, Y.Z., and Miao, G.P. Vertex Patterns and Roll Damping on Various Cross Sections of Ship[J]. China Ocean Engineering, 2000, 14:185~192.
[118] Chakrabarti, S. Empirical calculation of roll damping for ships and barges[J]. Ocean Engineering Journal, 2001, 28:915~932.
[119]张怀新,缪国平,刘应中,朱天宇.三维振荡船体贴体网格的生成[J].上海交通大学学报. 1996, 30(10): 28~34.
[120]张怀新,朱天宇,缪国平,刘应中.摇荡物体周围粘性流的数值模拟[J].上海交通大学学报. 1997, 31(11): 121~126.
[121]张怀新,刘应中,缪国平.船体各种剖面的横摇阻尼与漩涡的形状[J].水动力学研究与进展. 2001, 16(3): 382~389.
[122]张怀新,刘应中,缪国平.带自由表面三维船体周围粘性流场的数值模拟[J].上海交通大学学报. 2001, 35(10): 1429~1432.
[123]潘雨村,张怀新.用密度函数法对自由表面进行数值模拟[J].水动力学研究与进展. 2004, 19(6): 726~732.
[124] Amsden, A.A. and Harlow. F.H. A Simplified MAC technique for Incompressible Fluid Calculations[J]. Journal of Computer Physics, 1970, 6:322~325.
[125] Vievelli, J.A. A Computing Method for Incompressible Flows Bounded by Moving Walls[J]. Journal of Computer Physics, 1971, 8:119~143.
[126] Chan, K.C. and Stree, R.L. A Computer Study of Finite Amplitude Water Wave[J]. Journal of Computer Physics, 1970, 6:68~94.
[127] Hino, T., Miyata, H. and Kajitani, H. A Numerical Method for Nonlinear Shallow Water Waver[J]. Journal of Society Naval Architects of Japan. 1983, 153:1~12. (in Japanese)
[128] Hirt, C.W. and Nicholos, B.D. Volume of Fluid (VOF) Method for Dynamics of Free Boundaries[J]. Journal of Computer Physics, 1981, 39:201~225.
[129] Prandtl, L. and Uber, D.A. Turbulenz. ZAMM[M]. 1925,5:136.
[130]Taylor, G.I. Statistical Theory of Turbulence[R]. Parts 1-4, Proc. of Royal Soc. of London, Series A.1935,151:421.
[131] Kolmogorov, A.N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers[R]. C.R.Acad.Sci., U.R.S.S..1941,30:301.
[132] Rodi, W. Turbulence Models and Their Application in Hydraulics[R]. IAHR-monograph, Delft.1980.
[133] Bedford, K., Findikakis, A., Larock, B.E., Rodi, W. and Street, R.L. Turbulence Modeling of Surface Water Flow and Transport[J]. Journal of Hydraulic Engineering, ASCE, 1988,114: 969~1073.
[134] Deardorff, J.W. A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Number[J]. Journal of Fluid Mechanics.1970, 41:453~480.
[135] Schumann, U. Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Amuli[J]. Journal of Computer Physics, 1975, 18:376~404.
[136] Smagorinsky, J. General Circulation Experiments with the Primitive Equations[J]. Monthly Weather Review, 1963, 91:99~164.
[137] Bardina, J. and Ferziger, J.H. Reynolds W C. Improved Subgrid Scale Models for Large Eddy Simulation[J]. AIAA, 1980:80~1357.
[138] Schumann, U. Doctoral Dissertation, Technical Univ. of Karlsruhe, Germany. Also KFK-Bericht 1854, Kemforschungszentrum Karlsruhe, 1973
[139] Moin, P. and Kim, J. Numerical Investigation of Turbulent Channel Flow[J]. Journal of Fluid Mechanics, 1982, 118:341~377.
[140] Kim, J., Moin, P. and Moser, R.D. Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number[J]. Journal of Fluid Mechanics, 1987, 177:133~166.
[141] Lilly, D.K. On the Application of the Eddy Viscosity Concept in the Inertial Subrange of Turbulence[R]. NCAR Manuscript No. 123, National Center for Atmospheric Research, Boulder, Colorado ,1966
[142] Germano, M. et al. A Dynamic Subgrid-Scale Eddy Viscosity Model[J]. Journal of Physics Fluids A, 1991, 3:1760~1765.
[143] Lilly, D.K. A Proposed Modification of the Germano Subgrid-Scale Closure Method[J]. Journal of Physics Fluids A, 1992, 4:633~635.
[144] Clark, R.A., Ferziger, J.H. and Reynolds, W.C. Evaluation of Subgrid-Scale Models Using an Accurately Simulated Turbulent Flow[J]. Journal of Mechanics. 1979, 91:1~16.
[145] McMillan, O.J. and Feriziger, J.H. Direct Testing of Subgrid-Scale Models[J]. AIAA 1979, 17: 1340~1346.
[146] Lesieur, M. and Metais, O. New Trends in Large-Eddy Simulations of Turbulence[J]. Annual Reviews, 1996, 28:45~82.
[147] Meneveau, C. and Katz, J. Scale-Invariance and Turbulence Models for Large-Eddy Simulation[J]. Annual Reviewing Fluid Mechanics, 2000, 32:1~32.
[148] Li, C.W. and Wang, J.H. Large Eddy Simulation of Free Surface Shallow-Water Flow[J]. International Journal for Numerical Method in Fluid, 2000, 34:31~46.
[149] Piomelli, U. and Balaras, E. Wall-Layer Models for Large-Eddy Simulation[J]. Annual Reviewing Fluid Mechanics, 2002, 34:349~374.
[150] Pitsch, H. Large-Eddy Simulation of Turbulent Combustion[J]. Annual Reviewing Fluid Mechanics, 2006, 38:453~482.
[151] You, D., Wang, M. and Moin, P. Large-Eddy Simulation of Flow Over a Wall-Mounted Hump with Separation Control[J]. AIAA, 2006, 44:2571~2577.
[152] Jouhaud, J.C., Gicquel, L.Y.M. and Enaux, B. Large-Eddy-Simulation Modeling for Aerothermal Predictions Behind a Jet in Crossflow[J]. AIAA, 2007, 45:2438~2447.
[153] Razafindralandy, D., Hamdouni, A. and Oberlack, M. Analysis and Development of Subgrid Turbulence Models Preserving the Symmetry Properties of the Navier–Stokes Equations[J]. European Journal of Mechanics B/Fluids, 2007, 26:531~550.
[154] Lam, K. and Lin, Y.F. Large Eddy Simulation of Flow Around Wavy Cylinders at a Subcritical Reynolds Number[J]. International Journal of Heat and Fluid Flow, 2008, 29: 1071~1088.
[155]戴正元.大涡模拟滤波网格尺度研究及其应用[D].上海,上海交通大学, 2007.
[156]朱仁庆.液体晃荡及其与结构的相互作用[D].无锡,中国船舶科学研究中心, 2001.
[157] Graham, E.W. and Rodriguez, A.M. The Characteristics of Fuel Motion Which Affect Airplane Dynamics[J]. Journal of Applied Mechanics, 1952, 19:381~388.
[158] Housner, G. Dynamic Pressure on Accelerated Fluid Containers[J]. Bulletin of the Seismological Society of America, 1957, 47:15~35.
[159] Abramson, H.N. The Dynamic Behavior of Liquid in Moving Containers[R]. NASA SP-106, 1966.
[160] Nakayama, T. and Washizu, K. The Boundary Element Method Applied to The Analysis of Two-Dimensional Nonlinear Sloshing Problems[J]. International Journal for Numerical Methods in Engineering, 1981, 17:1631~1646.
[161] Mikelis, N.E. and Journee, J.M. Experimental and Numerical Simulations of Sloshing Behavior in Liquid Tanks and its Effect on Ship Motion[R]. National Conference on Numerical Methods for Transient and Coupled Problem, Venice, Italy, 1984.
[162] Hwang, J.H., Kim, I.S., Seol, Y.S. and Lee, S.C. Numerical Simulation of Liquid Sloshing in 3-Dimensional Tanks[J]. Journal of Computers and Structures, 1992, 44:339~342.
[163] Armenio, V. and Rocca, L.M. On the Analysis of Sloshing of Water in Rectangular Containers: Numerical Study and Experimental Validation[J]. Ocean Engeering, 1996, 23:705~739.
[164] Chen, W., Haroun, M.A. and Liu, F. Large Amplitude Liquid Sloshing in Seismically Excited Tank[J]. Earthquake Engeering and Stractural Dynamics, 1996, 25:653~669.
[165] Carious, A. nd Casella, G. Liquid Sloshing in Ship Tanks: a Comparative Study of Numerical Simulation[J]. Marine Structures, 1999, 12:183~198.
[166] Nielsen, K.B. Numerical Prediction of Green Water Loads on Ship[D]. Technical University of Denmark, Denmark, 2003.
[167] Yu, K. Level-Set RANS Method for Sloshing and Green Water Simulations[D]. Texas A&M University, Texas, 2007.
[168] Delorme, L. et al. A Set of Canonical Problems in Sloshing, Part I Pressure Field in Forced Roll Comparison Between Experimental Results and SPH[J]. Ocean Engineering, 2009, 36:168~178.
[169] Olsen, H. and Johnsen, K.R. Nonlinear Sloshing in Rectangular Tanks. A Pilot Study on The Applicability of Analytical Models[R]. Det Norske Veritas Report 74-72-S, vol. II, 1975.
[170] Lohner, R., Yang, C. and Onate, E. Simulation of Flows with Violent Free Surface Motion and Moving Objects Using Unstructured Grids[J]. International Journal for Numerical Methods inFluids, 2007, 53:1315~1338.
[171] Landrini, M., Colagorossi, A. and Faltisen, O.M. Sloshing in 2-D Flows by The SPH Method[J]. Proceedings of the 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea, 2003.
[172] Bass, R. et al. Modeling Criteria for Scaled LNG Sloshing Experiments[J]. Transactions of the ASME, 1985, 107:272~280.
[173] Peregrine, D. Water-Wave Impact on Walls[J]. Annual Review of Fluid Mechanics, 2003: 35: 23~43.
[174] Lee, Y.B. et al. An Experimental Study of Impulsive Sloshing Load Acting on LNG Tank[J]. Proceedings of the 16th ISOPE, 2006.
[175] Akyildrz, H. and Unal, N.E. Sloshing in a Three-Dimensional Rectangular Tank Numerical Simulation and Experimental Validation[J]. Ocean Engineering, 2006, 33:2135~2149.
[176] Lee, D.H. et al. A Parametric Sensitivity Study on LNG Tank Sloshing Loads by Numerical Simulations[J]. Ocean Engineering, 2007, 34:3~9.
[177] Faltisen, O.M. and Timokha, A.N. An Adaptive Multimodal Approach to Nonlinear Sloshing in a Rectangular Tank[J]. Journal of Fluid Mechanics, 2001, 432:167~200.
[178] Faltisen, O.M. and Timokha, A.N. Asymptotic Modal Approximation of Nonlinear Resonant Sloshing in a Rectangular Tank with Small Fluid Depth[J]. Journal of Fluid Mechanics, 2002, 470:319~357.
[179] Faltisen, O.M., Rognebakke, O.F. and Timokha, A.N. Resonant Three-Dimensional Nonlinear Sloshing in a Square-Base Basin[J]. Journal of Fluid Mechanics, 2003, 487:1~42.
[180] Faltisen, O.M., Rognebakke, O.F. and Timokha, A.N. Classification of Three-Dimensional Nonlinear Sloshing in a Square-Base Tank with Finite Depth[J]. Journal of Fluids and Structures, 2005, 20:81~103.