基于缓解压力振荡MPS法的数值水池研究
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摘要
在计算流体力学领域中,对于大变形自由表面的问题研究一直在不断的进展。计算流体力学领域中的数值模拟方法主要分为无网格法和网格法两种,其中无网格法在解决表面问题具有得天独厚的优势。移动粒子半隐式法(Moving-Particle Semi-Implicit Method, MPS)是一种新的基于拉格朗日(Lagrange)粒子的无网格方法,MPS法着眼于跟踪粒子的运动学和动力学性质变化过程。因此MPS法不需要建立网格,尤其在模拟大变形自由表面的问题可以简化网格布置的过程,得到比较理想的模拟效果。?
MPS法虽然在模拟自由液体自由表面有一定的优势,但是自身的压力振荡性问题严重限制了此方法在工程上的应用。在MPS法的研究过程中许多人做了相关缓解压力的研究,但效果都不是特别好。本文从MPS压力产生的原因着手,在MPS法的压力泊松方程中加入了在计算流体力学领域中常用的保证流体不可压缩性的散度为0的条件共同控制压力方程,减少压力的振荡性。利用缓解压力振荡的改进MPS法和原方法进行了溃坝模型和液舱晃荡模型进行模拟验证。通过这两个算例的对比验证了缓解压力振荡的改进MPS法在数值模拟过程中成功的缓解了压力振荡现象。
波浪是船舶与海洋工程类和港口航道与近海工程中最重要的动力因素之一。数值波浪水池是研究波浪的主要数值手段之一,既避免了建立物理模型的费时费力,同时数值波浪水池在空间尺度、可控制性方面具有更大的扩展性。本文根据上海交通大学的船模拖曳水池的模型进行等比例缩小,成功地利用MPS法的初始模拟完成了数值水池的建立。
在数值模拟领域中,大涡模拟是一种最新的解决湍流这种最常见的流动模式的研究方法,效果比较不错。本文将MPS法大涡模拟成功的应用在新建立的数值水池上,并进行造波模拟。针对MPS法大涡模拟造成的水池波浪振荡过大的问题,利用新开发的缓解压力振荡的改进MPS法大涡模拟进行造波模拟,成功的控制了数值水池造波压力过大的问题,得到不错的造波效果。同时在MPS法大涡模拟的造波过程中针对不动核函数进行造波模拟的比较,得出KF1核函数适用于改进MPS法大涡模拟的造波模拟。最后利用KF1核函数的数值造波模拟研究了改进方法中的松弛因子对于数值造波的影响。
In the Computational Fluid Dynamics, the flows including large deforming free surface have been studied for a long time. The main numerical simulation methods in CFD are grid method and meshless method and meshless method have an advantage on resolving flow problem with free surface. Moving-Particle Semi-Implicit Method (MPS) is a new meshless numerical method which bases on Lagrange particle, which trace the changing feature of dynamic and kinematic. Due to the advantage in free surface simulation, the MPS method plays more and more important role in numerical research.?
Although MPS have a good result in simulation with free surface, the pressure fluctuation restricts the application in engineering. People had some study on reduce the pressure fluctuation, but they did not get some good results. This paper focuses on the reason on the pressure oscillation, therefore combine the pressure Poisson equation with divergence-free condition which is usually used to ensure the incompressibility of flows. There are two kinds of cases being numerical simulated which are water collapse and ship roll sloshing. Comparing to the original MPS method, the result from the new method is real, so that the new method has good practicability and reliability.
Wave is one of the most important dynamic factors in the Naval architecture and Ocean Engineering and Coastal Engineering. It is used to establish model to solve such problem. Numerical wave tank had become a main way to study waves. It can not only save huge amout of time than physical model, but also have more expansibility on scale and controllability. A numerical wave tank has been build successfully based on ship model test towing tank in SJTU.
Large Eddy Simulation(LES) is a new method proposed to solve turbulent flows which is common in the world and it has good effect. LES is used in the new numerical wave tank to generate wave numerically. The constract has been made based on different kernel function and KF1 is suitable for numerical wave generation. This paper combines LES with new modified MPS to generate wave numerically to reduce the pressure oscillation successfully. At last, the influence of relaxation factor to the numerical wave has been studied based on KF1 kernel function.
MPS法虽然在模拟自由液体自由表面有一定的优势,但是自身的压力振荡性问题严重限制了此方法在工程上的应用。在MPS法的研究过程中许多人做了相关缓解压力的研究,但效果都不是特别好。本文从MPS压力产生的原因着手,在MPS法的压力泊松方程中加入了在计算流体力学领域中常用的保证流体不可压缩性的散度为0的条件共同控制压力方程,减少压力的振荡性。利用缓解压力振荡的改进MPS法和原方法进行了溃坝模型和液舱晃荡模型进行模拟验证。通过这两个算例的对比验证了缓解压力振荡的改进MPS法在数值模拟过程中成功的缓解了压力振荡现象。
波浪是船舶与海洋工程类和港口航道与近海工程中最重要的动力因素之一。数值波浪水池是研究波浪的主要数值手段之一,既避免了建立物理模型的费时费力,同时数值波浪水池在空间尺度、可控制性方面具有更大的扩展性。本文根据上海交通大学的船模拖曳水池的模型进行等比例缩小,成功地利用MPS法的初始模拟完成了数值水池的建立。
在数值模拟领域中,大涡模拟是一种最新的解决湍流这种最常见的流动模式的研究方法,效果比较不错。本文将MPS法大涡模拟成功的应用在新建立的数值水池上,并进行造波模拟。针对MPS法大涡模拟造成的水池波浪振荡过大的问题,利用新开发的缓解压力振荡的改进MPS法大涡模拟进行造波模拟,成功的控制了数值水池造波压力过大的问题,得到不错的造波效果。同时在MPS法大涡模拟的造波过程中针对不动核函数进行造波模拟的比较,得出KF1核函数适用于改进MPS法大涡模拟的造波模拟。最后利用KF1核函数的数值造波模拟研究了改进方法中的松弛因子对于数值造波的影响。
In the Computational Fluid Dynamics, the flows including large deforming free surface have been studied for a long time. The main numerical simulation methods in CFD are grid method and meshless method and meshless method have an advantage on resolving flow problem with free surface. Moving-Particle Semi-Implicit Method (MPS) is a new meshless numerical method which bases on Lagrange particle, which trace the changing feature of dynamic and kinematic. Due to the advantage in free surface simulation, the MPS method plays more and more important role in numerical research.?
Although MPS have a good result in simulation with free surface, the pressure fluctuation restricts the application in engineering. People had some study on reduce the pressure fluctuation, but they did not get some good results. This paper focuses on the reason on the pressure oscillation, therefore combine the pressure Poisson equation with divergence-free condition which is usually used to ensure the incompressibility of flows. There are two kinds of cases being numerical simulated which are water collapse and ship roll sloshing. Comparing to the original MPS method, the result from the new method is real, so that the new method has good practicability and reliability.
Wave is one of the most important dynamic factors in the Naval architecture and Ocean Engineering and Coastal Engineering. It is used to establish model to solve such problem. Numerical wave tank had become a main way to study waves. It can not only save huge amout of time than physical model, but also have more expansibility on scale and controllability. A numerical wave tank has been build successfully based on ship model test towing tank in SJTU.
Large Eddy Simulation(LES) is a new method proposed to solve turbulent flows which is common in the world and it has good effect. LES is used in the new numerical wave tank to generate wave numerically. The constract has been made based on different kernel function and KF1 is suitable for numerical wave generation. This paper combines LES with new modified MPS to generate wave numerically to reduce the pressure oscillation successfully. At last, the influence of relaxation factor to the numerical wave has been studied based on KF1 kernel function.
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]王献孚,周树信,陈泽梁等.船舶计算流体力学[M].上海:上海交通大学出版社. 1992.
[3]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.
[4]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.
[5]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.
[6]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.
[7]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.
[8] 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.
[9] Li, S.F. and Liu, W.K. Meshfree and Particle Methods and Their Applications[J]. Applied Mechanics Review. 2002, 55:1~34.
[10] Harlow, F.H. The Particle-In-Cell Computing Method for Fluid Dynamics[J]. Methods in Computational Physics. 1957, 3: 319~326.
[11] Harlow, F.H. and Welch, J. Numerical Calculation of Time-Dependent Viscous Incompressible Flow[J]. Physics of fluids. 1965, 8: 2182~2189.
[12] 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.
[13] 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.
[14] Belytschko, T. Lu, Y.Y. and Gu, L. Element-Free Galerkin Methods[J]. International Journal for Numerical Method in Engineering. 1994, 37: 229~256.
[15]仇秩,由长福,祁海鹰,徐旭常.粘性不可压缩流场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.
[16]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.
[17]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.
[18]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.
[19]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.
[20]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.
[21] Lucy, L.B. A Numerical Approach to the Testing of the Fission Hypothesis[J]. The Astron Journal. 1977, 8: 1013~1024.
[22] Mongahan, J. J. Shock Simulation by the Partiele Mehtod SPH[J]. Journal of Compute Physics. 1983, 52: 374~389.
[23] Monaghan, J.J. On the Problem of Penetration in Particle Methods[J]. Journal Computational Physics. 1989, 82: 1~15.
[24] Monaghan, J.J. Simulating Free Surface Flows with SPH[J]. Journal Computational Physics. 1994, 110: 399~406.
[25] 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.
[26] Monaghan, J. J., Kocharyan, A. SPH Simulation of Multi-phase Flow[J]. Computer Physics Communications. 1995, 87:225~235.
[27] 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.
[28] Benz, W. Numerical Modeling of Nonlinear Stellar Pulsation: Problems and Prospects. Kluwer Academic, Boston, MA, 1990: 269.
[29] Petschek, A. G.., Libersky, L. D. Cylindral Smoothed Particle Hydrodynamics[J]. Journal of Computer Physics. 1993, 109: 76~83.
[30] Libersky, L. D., Petschek, A. G.. High Strain Lagrangian Hydrodynmaics-A Three Dimensional SPH Code for Dynamics Material Response[J]. Journal of Computer Physics. 1993, 109: 67~75.
[31] 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.
[32] Hayhurst, C. J., Clegg, R. A. Cylindrical Symmetical SPH Simulations of Hypervelocity Impactson Thin Plates[J]. International Journal of Impact Engineering. 1997, 20: 337~348.
[33]刘瑛琦,基于SPH方法的数值波浪水槽研究[D].河海大学,河海大学海洋学院:2006,9-64.
[34] 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.
[35]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.
[36]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.
[37]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
[38]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
[39]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.
[40]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.
[41] 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.
[42] Koshizuka, S. and Oka, Y. Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid[J]. Nuclear Science and Engineering. 1996, 123: 421~434.
[43] Koshizuka S., Ikeda, H. and Oka, Y. Numerical Analysis of Fragmentation Mechanisms in Vapor Explosions[J]. Nuclear Engineering and Design. 1999, 189: 426~433.
[44] Gotoh, H. and Sakai, T. Largrangian Simulation of Breaking Waves Using Particle Method[J]. Coast Engineering Journal. 1999, 41: 303~326.
[45] 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.
[46]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.
[47]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.
[48] 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)
[49] 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)
[50] 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)
[51] Sueyoshi, M. Numerical Simulation of Extreme Motions of a Floating Body by MPS Method[J]. 2004, IEEE.
[52] 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)
[53] Guo, J. and Tao, Z. Modified Moving Particle Semi-Implicit Meshless Method for Incompressible Fluids[J]. Journal of Thermal Science. 2004, 13: 226~234.
[54] Gotoh, H. et al. Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall[J]. Coastal Engineering Journal, 2005, 47:157~181.
[55] 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.
[56] Wang, Q., Zheng, Y., Chen, C., Fujimoto, T. and Chiba, N. Efficient Rendering of Breaking Waves Using MPS Method[J]. Journal of Zhejiang University Science A. 2006, 7:1018~1025.
[57] Shao, S.D. and Gotoh, H. Turbulence Particle Models for Tracking Free Surfaces[J]. Journal of Hydraulic Research. 2005, 43: 276~289.
[58] Ataie-Ashtiani, B. and Farhadi, L. A Stable Moving-Particle Semi-Implicit Method for Free Surface Flows[J]. Fluid Dynamics. 2006, 38: 241~256.
[59] 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.
[60] 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.
[61] Sueyoshi, M., Kihara, H. and Kashiwagi, M. Numerical Simulation of Deck Wetness for a 2D Pontoon-Type Floating Structure[J]. 2008, IEEE.
[62] 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.
[63] 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.
[64] 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.
[65] 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)
[66] 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.
[67]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.
[68]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.
[69]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.
[70]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.
[71]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.
[72]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.
[73]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.
[74]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.
[75]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.
[76]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.
[77]潘徐杰.基于大涡模拟的移动粒子半隐式法研究及其应用[D].上海:上海交通大学船舶海洋与建筑工程学院. 2009, 16-182.
[78]潘徐杰,张怀新.移动粒子半隐式法晃荡模拟中压力震荡现象研究[J].水动力学研究与进展. 2008 Vol 23,No 4: 453~463.
[79]田中正幸,益永孝幸.疑似壓縮性效果にょゐMPS法の安定化と壓力の平滑化[J]. Transactions of JSCES, 2008,20080025(2008).
[80] Delorme, L. et al. A Set of Canonical Problems in Sloshing, Part I Pressure Field in Forced RollComparison Between Experimental Results and SPH[J]. Ocean Engineering, 2009, 36:168~178.
[81]尹振军.无网格水波动力学数值模拟理论及应用研究[D].天津:天津大学港口海岸与近海工程. 2004, 1-61.
[82]熊赞.基于光滑粒子半隐式方法水流数学模型理论及应用研究[D].天津:天津大学港口海岸与近海工程. 2006, 1-59.
[83]王永学,无反射造波数值水槽[J].水动力学研究与进展, Ser A., 1994, 9(2):205-212.
[84]刘海青,赵子丹,数值波浪水槽的建立与验证[J].水动力学研究与进展, Ser A., 1999, 14(1): 8-15.
[85]孙大鹏,李玉成,数值水槽内的阻尼消波和波浪变形计算[J].海洋工程,2000, 18(2):46-51.
[86]李炎保,黄凌燕,谷汉斌,不完全立波的二维数值波浪水槽模拟[J].海洋学报,2002, 24(4):105- 110.
[87]高学平,曾广冬,张亚,不规则数值波浪水槽的造波和阻尼消波[J].海洋学报, 2002, 24(2):127-132.
[88]石瑞祥,周宗仁,尹彰,二维数值造波水槽不规则波之数值研究[J].燕山大学学报,2004, 28(2):172-178.
[89]許泰文,近岸水動力學[M],中國土木工程學會.臺北:成陽出版股份有限公司,2003.
[90] Smagorinsky, J. General Circulation Experiments with the Primitive Equations[J]. Monthly Weather Review, 1963, 91:99~164.
[91] 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.
[92] 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.
[93]苏铭德,黄索逸.计算流体力学基础(第一版)[M].北京:清华大学出版社,1997.
[94]李家春,谢正桐.植被层湍流的大涡模拟[J].力学学报,1999,7(4):406-414.
[95] Kraichnan R H. Eddy viscosity in two and three dimensions[J]. J. Atmos. Sci., 1976, (33): 15-21.
[96]Chollet J P, Lesieur M.Parmneterisation of small scales of three-dimensional isotropic turbulence utilizing spectralclosums[J]. J. Atmos. Sci., 1981, (33): 27-47.
[97] Germano, M. et al. A Dynamic Subgrid-Scale Eddy Viscosity Model[J]. Journal of Physics Fluids A, 1991, 3:1760~1765.
[98] Lesieur M, Metais O. Spectral large-eddy simulation of isotmpie and stably-stratified turbulence[J]. J Fluid Mech, 1992, (239): 157-194.
[99] Bardina, J. and Ferziger, J.H. Reynolds W C. Improved Subgrid Scale Models for Large Eddy Simulation[J]. AIAA, 1980:80~1357.
[100] Zang Y, Street R, Koseff J R. A dynamic mixed subgridscale model and its application to turbulent recirculating flows[J]. Phys Fluids A, 1993, (5): 3186-3196.
[101] Bardina J, Ferziger J H, Reynolds W C. Improved turbulence models based on large eddy simulation of homogeneous incompressible turbulence[R]. Stanford Univ Report TF-19, 1983.
[102]荆宁字,陆夕云等.分层剪切湍流大涡模拟的一种动力学亚格子尺度模型[J].中国科学A辑. 2000, 30(2): 145-153.
[103]严红,苏铭德.激励小尺度模式在湍流圆管射流中的作用[J].力学学报,2000,9(5):513-522.
[104]王汉青,王志勇,寇广孝.大涡模拟理论进展及其在工程中的应用[J].流体机械,2004, 32(7): 23-27.
[105] 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.
[106] Schumann, U. Doctoral Dissertation, Technical Univ. of Karlsruhe, Germany. Also KFK-Bericht 1854, Kemforschungszentrum Karlsruhe, 1973
[107] Moin, P. and Kim, J. Numerical Investigation of Turbulent Channel Flow[J]. Journal of Fluid Mechanics, 1982, 118:341~377.
[2]王献孚,周树信,陈泽梁等.船舶计算流体力学[M].上海:上海交通大学出版社. 1992.
[3]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.
[4]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.
[5]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.
[6]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.
[7]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.
[8] 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.
[9] Li, S.F. and Liu, W.K. Meshfree and Particle Methods and Their Applications[J]. Applied Mechanics Review. 2002, 55:1~34.
[10] Harlow, F.H. The Particle-In-Cell Computing Method for Fluid Dynamics[J]. Methods in Computational Physics. 1957, 3: 319~326.
[11] Harlow, F.H. and Welch, J. Numerical Calculation of Time-Dependent Viscous Incompressible Flow[J]. Physics of fluids. 1965, 8: 2182~2189.
[12] 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.
[13] 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.
[14] Belytschko, T. Lu, Y.Y. and Gu, L. Element-Free Galerkin Methods[J]. International Journal for Numerical Method in Engineering. 1994, 37: 229~256.
[15]仇秩,由长福,祁海鹰,徐旭常.粘性不可压缩流场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.
[16]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.
[17]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.
[18]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.
[19]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.
[20]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.
[21] Lucy, L.B. A Numerical Approach to the Testing of the Fission Hypothesis[J]. The Astron Journal. 1977, 8: 1013~1024.
[22] Mongahan, J. J. Shock Simulation by the Partiele Mehtod SPH[J]. Journal of Compute Physics. 1983, 52: 374~389.
[23] Monaghan, J.J. On the Problem of Penetration in Particle Methods[J]. Journal Computational Physics. 1989, 82: 1~15.
[24] Monaghan, J.J. Simulating Free Surface Flows with SPH[J]. Journal Computational Physics. 1994, 110: 399~406.
[25] 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.
[26] Monaghan, J. J., Kocharyan, A. SPH Simulation of Multi-phase Flow[J]. Computer Physics Communications. 1995, 87:225~235.
[27] 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.
[28] Benz, W. Numerical Modeling of Nonlinear Stellar Pulsation: Problems and Prospects. Kluwer Academic, Boston, MA, 1990: 269.
[29] Petschek, A. G.., Libersky, L. D. Cylindral Smoothed Particle Hydrodynamics[J]. Journal of Computer Physics. 1993, 109: 76~83.
[30] Libersky, L. D., Petschek, A. G.. High Strain Lagrangian Hydrodynmaics-A Three Dimensional SPH Code for Dynamics Material Response[J]. Journal of Computer Physics. 1993, 109: 67~75.
[31] 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.
[32] Hayhurst, C. J., Clegg, R. A. Cylindrical Symmetical SPH Simulations of Hypervelocity Impactson Thin Plates[J]. International Journal of Impact Engineering. 1997, 20: 337~348.
[33]刘瑛琦,基于SPH方法的数值波浪水槽研究[D].河海大学,河海大学海洋学院:2006,9-64.
[34] 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.
[35]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.
[36]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.
[37]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
[38]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
[39]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.
[40]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.
[41] 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.
[42] Koshizuka, S. and Oka, Y. Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid[J]. Nuclear Science and Engineering. 1996, 123: 421~434.
[43] Koshizuka S., Ikeda, H. and Oka, Y. Numerical Analysis of Fragmentation Mechanisms in Vapor Explosions[J]. Nuclear Engineering and Design. 1999, 189: 426~433.
[44] Gotoh, H. and Sakai, T. Largrangian Simulation of Breaking Waves Using Particle Method[J]. Coast Engineering Journal. 1999, 41: 303~326.
[45] 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.
[46]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.
[47]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.
[48] 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)
[49] 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)
[50] 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)
[51] Sueyoshi, M. Numerical Simulation of Extreme Motions of a Floating Body by MPS Method[J]. 2004, IEEE.
[52] 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)
[53] Guo, J. and Tao, Z. Modified Moving Particle Semi-Implicit Meshless Method for Incompressible Fluids[J]. Journal of Thermal Science. 2004, 13: 226~234.
[54] Gotoh, H. et al. Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall[J]. Coastal Engineering Journal, 2005, 47:157~181.
[55] 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.
[56] Wang, Q., Zheng, Y., Chen, C., Fujimoto, T. and Chiba, N. Efficient Rendering of Breaking Waves Using MPS Method[J]. Journal of Zhejiang University Science A. 2006, 7:1018~1025.
[57] Shao, S.D. and Gotoh, H. Turbulence Particle Models for Tracking Free Surfaces[J]. Journal of Hydraulic Research. 2005, 43: 276~289.
[58] Ataie-Ashtiani, B. and Farhadi, L. A Stable Moving-Particle Semi-Implicit Method for Free Surface Flows[J]. Fluid Dynamics. 2006, 38: 241~256.
[59] 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.
[60] 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.
[61] Sueyoshi, M., Kihara, H. and Kashiwagi, M. Numerical Simulation of Deck Wetness for a 2D Pontoon-Type Floating Structure[J]. 2008, IEEE.
[62] 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.
[63] 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.
[64] 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.
[65] 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)
[66] 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.
[67]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.
[68]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.
[69]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.
[70]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.
[71]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.
[72]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.
[73]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.
[74]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.
[75]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.
[76]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.
[77]潘徐杰.基于大涡模拟的移动粒子半隐式法研究及其应用[D].上海:上海交通大学船舶海洋与建筑工程学院. 2009, 16-182.
[78]潘徐杰,张怀新.移动粒子半隐式法晃荡模拟中压力震荡现象研究[J].水动力学研究与进展. 2008 Vol 23,No 4: 453~463.
[79]田中正幸,益永孝幸.疑似壓縮性效果にょゐMPS法の安定化と壓力の平滑化[J]. Transactions of JSCES, 2008,20080025(2008).
[80] Delorme, L. et al. A Set of Canonical Problems in Sloshing, Part I Pressure Field in Forced RollComparison Between Experimental Results and SPH[J]. Ocean Engineering, 2009, 36:168~178.
[81]尹振军.无网格水波动力学数值模拟理论及应用研究[D].天津:天津大学港口海岸与近海工程. 2004, 1-61.
[82]熊赞.基于光滑粒子半隐式方法水流数学模型理论及应用研究[D].天津:天津大学港口海岸与近海工程. 2006, 1-59.
[83]王永学,无反射造波数值水槽[J].水动力学研究与进展, Ser A., 1994, 9(2):205-212.
[84]刘海青,赵子丹,数值波浪水槽的建立与验证[J].水动力学研究与进展, Ser A., 1999, 14(1): 8-15.
[85]孙大鹏,李玉成,数值水槽内的阻尼消波和波浪变形计算[J].海洋工程,2000, 18(2):46-51.
[86]李炎保,黄凌燕,谷汉斌,不完全立波的二维数值波浪水槽模拟[J].海洋学报,2002, 24(4):105- 110.
[87]高学平,曾广冬,张亚,不规则数值波浪水槽的造波和阻尼消波[J].海洋学报, 2002, 24(2):127-132.
[88]石瑞祥,周宗仁,尹彰,二维数值造波水槽不规则波之数值研究[J].燕山大学学报,2004, 28(2):172-178.
[89]許泰文,近岸水動力學[M],中國土木工程學會.臺北:成陽出版股份有限公司,2003.
[90] Smagorinsky, J. General Circulation Experiments with the Primitive Equations[J]. Monthly Weather Review, 1963, 91:99~164.
[91] 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.
[92] 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.
[93]苏铭德,黄索逸.计算流体力学基础(第一版)[M].北京:清华大学出版社,1997.
[94]李家春,谢正桐.植被层湍流的大涡模拟[J].力学学报,1999,7(4):406-414.
[95] Kraichnan R H. Eddy viscosity in two and three dimensions[J]. J. Atmos. Sci., 1976, (33): 15-21.
[96]Chollet J P, Lesieur M.Parmneterisation of small scales of three-dimensional isotropic turbulence utilizing spectralclosums[J]. J. Atmos. Sci., 1981, (33): 27-47.
[97] Germano, M. et al. A Dynamic Subgrid-Scale Eddy Viscosity Model[J]. Journal of Physics Fluids A, 1991, 3:1760~1765.
[98] Lesieur M, Metais O. Spectral large-eddy simulation of isotmpie and stably-stratified turbulence[J]. J Fluid Mech, 1992, (239): 157-194.
[99] Bardina, J. and Ferziger, J.H. Reynolds W C. Improved Subgrid Scale Models for Large Eddy Simulation[J]. AIAA, 1980:80~1357.
[100] Zang Y, Street R, Koseff J R. A dynamic mixed subgridscale model and its application to turbulent recirculating flows[J]. Phys Fluids A, 1993, (5): 3186-3196.
[101] Bardina J, Ferziger J H, Reynolds W C. Improved turbulence models based on large eddy simulation of homogeneous incompressible turbulence[R]. Stanford Univ Report TF-19, 1983.
[102]荆宁字,陆夕云等.分层剪切湍流大涡模拟的一种动力学亚格子尺度模型[J].中国科学A辑. 2000, 30(2): 145-153.
[103]严红,苏铭德.激励小尺度模式在湍流圆管射流中的作用[J].力学学报,2000,9(5):513-522.
[104]王汉青,王志勇,寇广孝.大涡模拟理论进展及其在工程中的应用[J].流体机械,2004, 32(7): 23-27.
[105] 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.
[106] Schumann, U. Doctoral Dissertation, Technical Univ. of Karlsruhe, Germany. Also KFK-Bericht 1854, Kemforschungszentrum Karlsruhe, 1973
[107] Moin, P. and Kim, J. Numerical Investigation of Turbulent Channel Flow[J]. Journal of Fluid Mechanics, 1982, 118:341~377.