电热化学炮内弹道过程无网格法数值模拟
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摘要
电热化学炮(ETCG)内弹道过程异常复杂,涉及两相流动力学、传热学、燃烧学、化学动力学、湍流力学、爆轰学等诸多学科,其中还存在多种物理强间断问题,如爆轰波、激波火焰波以及传火孔高速射流等,又由于装药结构和初始装填条件的原因造成药筒间的间隙及弹后自由空间等不连续问题从而形成空间上强间断面。这些物理间断和空间间断给传统的基于网格的数值模拟方法的应用带来了很大的困难。而无网格法最大的优点在于它不需要在问题域中划分网格,这就摆脱了不连续性对问题的束缚(如网格的重构等),保证了求解精度。
光滑粒子流体动力学(SPH)数值模拟方法是一种无网格粒子法,它在流体力学和固体力学领域都有广泛的应用,比如在弹性流、磁流体力学、多相流动和金属成型模拟等方面。SPH方法的另外一个重要应用是模拟高能炸药燃烧爆炸现象,是瞬态物理领域新的重要的一种数值模拟方法。
本文用SPH方法对固体化学工质电热化学炮的内弹道过程进行数值模拟,这是一个二维轴对称气-固两相流瞬态物理过程。在结合流体力学基本方程组与电热化学炮内弹道基本假设的基础上,用Fortran语言编写了内弹道过程SPH计算程序,对内弹道的一些重要参数,温度、压力和空隙率等随时间、空间的变化进行了模拟分析。计算结果表明,用SPH法编写的内弹道计算程序可行,其结果与实验数据基本吻合。
Interior ballistic process of Electrothermal Chemical Guns(ETCG) is extremely complex, which involves two-phase flow dynamics, heat transfer, combustion, chemical kinetics, turbulence mechanics, detonation and many other subjects.There are a variety of physical intensity intermittent problems, such as the detonation wave, shock wave and flame pass the fire-hole high-speed jet, etc. and the gap between the cartridges and discontinuity of playing after the free space which form a strong discontinuity in space is caused by the charging structure and the initial loading condition.Great difficulties is brougth by continuous and intermittent physical space for the traditional method of numerical simulation application based on grid. The biggest advantages of the non-grid method of are that they don't need mesh in the problem domain,which is free from the shackles of the discontinuity of the problem (such as the reconstruction of the grid, etc.),and ensure the solution accuracy.
Smooth particle hydrodynamics (SPH) simulation method is a meshless particle method, which has a wide range of applications in the field of fluid mechanics and solid mechanics,such as the elastic flow, magnetic hydrodynamics, multiphase flow and metal forming simulation and so on.Another important application of The SPH method is simulationing high explosive combustion and explosion phenomena,which is an important new numerical simulation method in transient physics.
This dissertation simulates the interior ballistic process of Electrothermal Chemical Guns with medium of solid-state chemistry by means of the SPH method, fluid within the process simulation,which is a transient physical processes of two-dimensional axisymmetric an gas-solid two-phase.The basic equations of fluid mechanics in combination with Electrothermal Chemical Guns interior ballistic assumption, based on written in Fortran computer program within the SPH interior ballistic process, interior ballistics of some important parameters, temperature, pressure, and porosity and other space-time changes in the simulation analysis. The results show that the computer program of trajectory written by the SPH method is feasible,and the results basically accord with experimental data.
光滑粒子流体动力学(SPH)数值模拟方法是一种无网格粒子法,它在流体力学和固体力学领域都有广泛的应用,比如在弹性流、磁流体力学、多相流动和金属成型模拟等方面。SPH方法的另外一个重要应用是模拟高能炸药燃烧爆炸现象,是瞬态物理领域新的重要的一种数值模拟方法。
本文用SPH方法对固体化学工质电热化学炮的内弹道过程进行数值模拟,这是一个二维轴对称气-固两相流瞬态物理过程。在结合流体力学基本方程组与电热化学炮内弹道基本假设的基础上,用Fortran语言编写了内弹道过程SPH计算程序,对内弹道的一些重要参数,温度、压力和空隙率等随时间、空间的变化进行了模拟分析。计算结果表明,用SPH法编写的内弹道计算程序可行,其结果与实验数据基本吻合。
Interior ballistic process of Electrothermal Chemical Guns(ETCG) is extremely complex, which involves two-phase flow dynamics, heat transfer, combustion, chemical kinetics, turbulence mechanics, detonation and many other subjects.There are a variety of physical intensity intermittent problems, such as the detonation wave, shock wave and flame pass the fire-hole high-speed jet, etc. and the gap between the cartridges and discontinuity of playing after the free space which form a strong discontinuity in space is caused by the charging structure and the initial loading condition.Great difficulties is brougth by continuous and intermittent physical space for the traditional method of numerical simulation application based on grid. The biggest advantages of the non-grid method of are that they don't need mesh in the problem domain,which is free from the shackles of the discontinuity of the problem (such as the reconstruction of the grid, etc.),and ensure the solution accuracy.
Smooth particle hydrodynamics (SPH) simulation method is a meshless particle method, which has a wide range of applications in the field of fluid mechanics and solid mechanics,such as the elastic flow, magnetic hydrodynamics, multiphase flow and metal forming simulation and so on.Another important application of The SPH method is simulationing high explosive combustion and explosion phenomena,which is an important new numerical simulation method in transient physics.
This dissertation simulates the interior ballistic process of Electrothermal Chemical Guns with medium of solid-state chemistry by means of the SPH method, fluid within the process simulation,which is a transient physical processes of two-dimensional axisymmetric an gas-solid two-phase.The basic equations of fluid mechanics in combination with Electrothermal Chemical Guns interior ballistic assumption, based on written in Fortran computer program within the SPH interior ballistic process, interior ballistics of some important parameters, temperature, pressure, and porosity and other space-time changes in the simulation analysis. The results show that the computer program of trajectory written by the SPH method is feasible,and the results basically accord with experimental data.
引文
[1]欧阳立新.电热化学发射技术的应用前景.弹道学报,1995,2(7)：92-96
[2]向阳,古刚,张建革.国外电热化学炮研究现状及发展趋势.舰船科学技术,2007,1(29)：159-162
[3]杨均匀,袁亚雄.火炮内弹道学的现状及发展.火炮发射与控制学报,2000,2：56-60
[4]孙江生,曹延杰,王莹.电热化学炮技术的动态研究.华北工学院学报,2000,2(21)：148-151
[5]谢玉树,袁亚雄,张小兵.等离子体与发射药相互作用的研究.火炮发射与控制学报,2001,1：55-58
[6]谢玉树,袁亚雄,张小兵.等离子体增强发射药燃烧的实验研究.火炸药学报,2001,3：10-12
[7]刘东尧,周彦煌.液体发射药电热化学发射内弹道一维两相流模型及数值模拟.爆炸与冲击,2002,2(22)：158-162
[8]薛幂炜,肖正刚,应三九,徐复铭.发射药等离子体点火与常规点火性能的比较.弹道学报,2009,3(21)：61-64
[9]李海元,栗保明,李鸿志.膛内等离子体点火及燃烧增强过程数值模拟.爆炸与冲击,2002,3(22)：229-236
[10]杨春霞,栗保明.包覆药等离子体点火及燃烧性能的实验研究.弹道学报,2007,4(19)：13-15
[11]张小兵,袁亚雄,谢玉树.等离子体点火密闭爆发器实验研究.火炸药学报,2003,2(26)：24-31
[12]李海元,栗保明,李鸿志.等离子体点火条件下火药燃速的实验研究.弹道学报,2007,2(19)：78-81
[13]李海元,栗保明,李鸿志.等离子体增强火炮发射性能的实验研究：弹箭与制导学报,2007,2(27)：297-312
[14]K. J. White, G. L. Katulka.Electrothermal Chemical plasma interaction with propellants. Proceedings of the 16th International Symposium on Ballistics,1996(1):387-396
[15]Haugh D C, Gilbert S. U.K. Electric Gun National Overview. IEEE Transactions on Magnetics,2003,39(1):18-21
[16]Klaus Kappen, Uwe H. Bauder. Calculation of plasma radiation transport for description of propellant ignition and simulation of interior ballistics in ETC Guns. IEEE Transaction on Magnetics,2001,37(1):169-172
[17]K. Kappen; U. H. Bauder. Simulation of plasma radiation in electrothermal-chemical accelerators. IEEE Transaction on Magnetics,1999,35
[18]Joseph R.Greig, Jon Earnhart,Neils Winsor. Investigation of plasma-augmented solid propellant interior ballistic processes. IEEE Transaction on Magnetics,1993,29(1): 555-560
[19]Glive R.Woodley, Steve J.Billett. Modeling Enhanced Gas Generation Rates in a 155-mm ETC Gun. IEEE Transaction on Magnetics,2001,37(1):207-210
[20]M. J. Taylor. Measurement of the Properties of Plasma from ETC Capillary Plasma Generators. IEEE Transactions on Magnetics,2001,37(1):194-198
[21]Martin Rott, Christian Artelt, and Till Hoeschen. Experimental Investigation of Hypervelocity Plasma Jets Generated With a Coaxial Arc Device. IEEE Transactions on Magnetics,2005,41(1):220-225
[22]R. J. Kennaugh, L. C. Woods. Optimization of an electro-thermal capillary. IEEE Transactions on Magnetics.1995,30(1):431-434
[23]陈林,周之奎,孙承纬.电热化学发射中等离子体发生器放电特性的实验研究.爆炸与冲击,1997,17(4)：375-381
[24]李海元.固体发射药燃速的等离子体增强机理及多维多相流数值模拟研究.南京理工大学,2006,[学位论文]
[25]李志飞.等离子体增强作用的内弹道过程数值模拟.南京理工大学,2008,[学位论文]
[26]谢玉树.等离子体与火药相互作用的研究.南京理工大学,2005,[学位论文]
[27]王争论.中心电弧等离子体发生器及其在电热化学炮中的应用研究.南京理工大学,2005,[学位论文]
[28]孟绍良.电热化学炮用脉冲电源及等离子体发生器电特性的研究.南京理工大学,2006,[学位论文]
[29]黄朝琴.无网格法理论与应用研究.中国石油大学,2007,[学位论文]
[30]张小华.无网格方法在计算流体力学中的应用研究.西北工业大学,2006,[学位论文]
[31]杨刚.光滑粒子法的改进及其若干典型应用.湖南大学,2010,[学位论文]
[32]邓方刚.柱坐标系下光滑粒子流体动力学数值模拟.国防科学技术大学,2002,[学位论文]
[33]陈建设.无网格SPH方法在板冲击问题中的数值模拟与应用研究.西北工业大学,2007,[学位论文]
[34]许庆新.基于SPH方法的冲击动力学若干问题研究.上海交通大学,2009,[学位论文]
[35]张强发.光滑质点流体动力学方法在结构分析中的应用.南京航空航天大学,2007,[学位论文1
[36]李九红,程玉民.无网格方法的研究进展与展望.力学季刊,2006,1(27)：143-152
[37]张雄,刘岩,马上.无网格法的理论及应用.力学进展,2009,1(39)：1-36
[38]C. R. Woodley and S. J. Billett. Modeling Enhanced Gas Generation Rates in a 155-mm ETC Gun. IEEE Transactions on Magnetics,2001,37(1):207-210
[39]D. Grune, D. Hensel. Combustion Behavior of LOVA-Solid-Propellant by Ignition with Hot Plasma Gases and its Influence on the Interior Ballistic Cycle. Proceedings of the 17th International Symposium on Ballistics,1998,1:359-366
[40]A. E. Wildegger-Gaissmaier, Gloria P. Wren, Ashvin Hosangadi. Modeling Flame Spread in Plasma Ignited Gun Charges. Proceedings of the 16th International Symposium on Ballistics 1996,123-133
[41]Klaus Kappen, Uwe H.Baude. Simulation of Plasma Radiation in Electroth-ermal Chemical Accelerator. IEEE Transaction on Magnetics,2009,1(39):1-36
[42]Noam Shafir, David Zoler, Shlomo Wald, Moshe Shapira.Reliable. Highly Reprod ucible Plasma Injectors for Electrothermal and Electrothermal-Chemical Launcher. IEEE Transaction on Magnetics,2005,41(1):355-359
[43]Koleczko A, Ehrhard W Schmid H, et al. Plasma ignition and combustion.2001, 195-202
[44]Yuan Pan, Kefu Liu, Baohua Liu. System Simulations and Experiments for Electrothermal-Chemical Guns Powered by Compulsators. IEEE Transaction on Magnetics,2003,39(1):427-439
[45]Shintate K, Sekine H. Numerical simulation of hypervelocity impact s of a projectile on laminated composite plate targets by means of improved SPH method[J]. Composites: A,2004,35:683-692.
[46]Petsehek A G, Libersky L D.Cylindral Smoothed Partiele Hydrodynamies.J ComPut Phys,1993,109:76-83
[47]金志明,宋明.火药床压缩模量及颗粒间应力.兵工学报,1990,1：28-35
[48]贝新源,岳宗五.三维SPH程序及其在斜高速碰撞问题的应用.计算物理,1997,14(2)：155-166
[49]龚凯,刘桦,王本龙.SPH固壁边界处理方法的改进.力学季刊,2008,29(4)：507-514
[50]郑坤,孙昭晨,张志明,周丰,赵西增.SPH数值模拟中边界处理方法及对比分析.水运工程,2009,8：23-27
[51]张刚明,王肖钧,王元博等.高速碰撞数值计算中的光滑粒子法.计算物理,2003,20(5)：447-454
[52]卞梁,王肖钧,章杰.高速碰撞数值计算中的SPH自适应粒子分布法.爆炸与冲击,2009,29(6)：607-612
[53]姚熊亮,陈娟,张阿漫,何江华.修正SPH方法在冲击波中的应用.哈尔滨工程大学学报,2010,31(1)：15-19
[54]刘东尧,郭海波,余永刚,周彦煌.毛细管消融等离子体及其射流压力特性研究.南京理工大学学报,2009,33(3)：348-370
[55]肖正刚,应三九,周伟良,徐复铭.低敏感高能发射药等离子体点火研究动态.含能材料,2008,16(5)：633-638
[56]狄加伟,杨敏涛,张明安,赵斌.电热化学发射技术在大口径火炮上的应用前景.火炮发射与控制学报,2010,(2)：24-27
[57]张军,邱沛蓉,董健年.电热化学炮脉冲形成网络分析及其参数设计.弹道学报,1997,9(1)：50-59
[58]翁春生,王浩.计算内弹道学.国防工业出版社,2006,1
[59]H.克里尔,M.萨默菲尔德.火炮内弹道.华东工程学院弹道研究所出版,1981
[60]金志明,袁亚雄.内弹道气动力原理.国防工业出版社,1983
[61]刘更,刘天祥,谢琴.无网格法及其应用.西北工业大学出版社,2005
[62]金志明,袁亚雄,宋明.现代内弹道学.北京理工大学,1992
[63]金志明.高速推进内弹道学.国防工业出版社,2001
[64]金志明,翁春生.高等内弹道学.高等教育出版社,2003
[65]金志明.枪炮内弹道学.北京理工大学出版社,2004
[66]刘大有.二相流体力学.
[67]周彦煌,王升晨.实用两相流内弹道学.第1版.兵器工业出版社,1990
[68]吴子牛.计算流体力学基本原理.科学出版社,2001
[69]董志勇.射流力学.科学出版社,2005
[70]韩旭,杨刚,强洪夫[译].光滑粒子流体动力学——一种无网格粒子法.湖南大学出版社,2005
[2]向阳,古刚,张建革.国外电热化学炮研究现状及发展趋势.舰船科学技术,2007,1(29)：159-162
[3]杨均匀,袁亚雄.火炮内弹道学的现状及发展.火炮发射与控制学报,2000,2：56-60
[4]孙江生,曹延杰,王莹.电热化学炮技术的动态研究.华北工学院学报,2000,2(21)：148-151
[5]谢玉树,袁亚雄,张小兵.等离子体与发射药相互作用的研究.火炮发射与控制学报,2001,1：55-58
[6]谢玉树,袁亚雄,张小兵.等离子体增强发射药燃烧的实验研究.火炸药学报,2001,3：10-12
[7]刘东尧,周彦煌.液体发射药电热化学发射内弹道一维两相流模型及数值模拟.爆炸与冲击,2002,2(22)：158-162
[8]薛幂炜,肖正刚,应三九,徐复铭.发射药等离子体点火与常规点火性能的比较.弹道学报,2009,3(21)：61-64
[9]李海元,栗保明,李鸿志.膛内等离子体点火及燃烧增强过程数值模拟.爆炸与冲击,2002,3(22)：229-236
[10]杨春霞,栗保明.包覆药等离子体点火及燃烧性能的实验研究.弹道学报,2007,4(19)：13-15
[11]张小兵,袁亚雄,谢玉树.等离子体点火密闭爆发器实验研究.火炸药学报,2003,2(26)：24-31
[12]李海元,栗保明,李鸿志.等离子体点火条件下火药燃速的实验研究.弹道学报,2007,2(19)：78-81
[13]李海元,栗保明,李鸿志.等离子体增强火炮发射性能的实验研究：弹箭与制导学报,2007,2(27)：297-312
[14]K. J. White, G. L. Katulka.Electrothermal Chemical plasma interaction with propellants. Proceedings of the 16th International Symposium on Ballistics,1996(1):387-396
[15]Haugh D C, Gilbert S. U.K. Electric Gun National Overview. IEEE Transactions on Magnetics,2003,39(1):18-21
[16]Klaus Kappen, Uwe H. Bauder. Calculation of plasma radiation transport for description of propellant ignition and simulation of interior ballistics in ETC Guns. IEEE Transaction on Magnetics,2001,37(1):169-172
[17]K. Kappen; U. H. Bauder. Simulation of plasma radiation in electrothermal-chemical accelerators. IEEE Transaction on Magnetics,1999,35
[18]Joseph R.Greig, Jon Earnhart,Neils Winsor. Investigation of plasma-augmented solid propellant interior ballistic processes. IEEE Transaction on Magnetics,1993,29(1): 555-560
[19]Glive R.Woodley, Steve J.Billett. Modeling Enhanced Gas Generation Rates in a 155-mm ETC Gun. IEEE Transaction on Magnetics,2001,37(1):207-210
[20]M. J. Taylor. Measurement of the Properties of Plasma from ETC Capillary Plasma Generators. IEEE Transactions on Magnetics,2001,37(1):194-198
[21]Martin Rott, Christian Artelt, and Till Hoeschen. Experimental Investigation of Hypervelocity Plasma Jets Generated With a Coaxial Arc Device. IEEE Transactions on Magnetics,2005,41(1):220-225
[22]R. J. Kennaugh, L. C. Woods. Optimization of an electro-thermal capillary. IEEE Transactions on Magnetics.1995,30(1):431-434
[23]陈林,周之奎,孙承纬.电热化学发射中等离子体发生器放电特性的实验研究.爆炸与冲击,1997,17(4)：375-381
[24]李海元.固体发射药燃速的等离子体增强机理及多维多相流数值模拟研究.南京理工大学,2006,[学位论文]
[25]李志飞.等离子体增强作用的内弹道过程数值模拟.南京理工大学,2008,[学位论文]
[26]谢玉树.等离子体与火药相互作用的研究.南京理工大学,2005,[学位论文]
[27]王争论.中心电弧等离子体发生器及其在电热化学炮中的应用研究.南京理工大学,2005,[学位论文]
[28]孟绍良.电热化学炮用脉冲电源及等离子体发生器电特性的研究.南京理工大学,2006,[学位论文]
[29]黄朝琴.无网格法理论与应用研究.中国石油大学,2007,[学位论文]
[30]张小华.无网格方法在计算流体力学中的应用研究.西北工业大学,2006,[学位论文]
[31]杨刚.光滑粒子法的改进及其若干典型应用.湖南大学,2010,[学位论文]
[32]邓方刚.柱坐标系下光滑粒子流体动力学数值模拟.国防科学技术大学,2002,[学位论文]
[33]陈建设.无网格SPH方法在板冲击问题中的数值模拟与应用研究.西北工业大学,2007,[学位论文]
[34]许庆新.基于SPH方法的冲击动力学若干问题研究.上海交通大学,2009,[学位论文]
[35]张强发.光滑质点流体动力学方法在结构分析中的应用.南京航空航天大学,2007,[学位论文1
[36]李九红,程玉民.无网格方法的研究进展与展望.力学季刊,2006,1(27)：143-152
[37]张雄,刘岩,马上.无网格法的理论及应用.力学进展,2009,1(39)：1-36
[38]C. R. Woodley and S. J. Billett. Modeling Enhanced Gas Generation Rates in a 155-mm ETC Gun. IEEE Transactions on Magnetics,2001,37(1):207-210
[39]D. Grune, D. Hensel. Combustion Behavior of LOVA-Solid-Propellant by Ignition with Hot Plasma Gases and its Influence on the Interior Ballistic Cycle. Proceedings of the 17th International Symposium on Ballistics,1998,1:359-366
[40]A. E. Wildegger-Gaissmaier, Gloria P. Wren, Ashvin Hosangadi. Modeling Flame Spread in Plasma Ignited Gun Charges. Proceedings of the 16th International Symposium on Ballistics 1996,123-133
[41]Klaus Kappen, Uwe H.Baude. Simulation of Plasma Radiation in Electroth-ermal Chemical Accelerator. IEEE Transaction on Magnetics,2009,1(39):1-36
[42]Noam Shafir, David Zoler, Shlomo Wald, Moshe Shapira.Reliable. Highly Reprod ucible Plasma Injectors for Electrothermal and Electrothermal-Chemical Launcher. IEEE Transaction on Magnetics,2005,41(1):355-359
[43]Koleczko A, Ehrhard W Schmid H, et al. Plasma ignition and combustion.2001, 195-202
[44]Yuan Pan, Kefu Liu, Baohua Liu. System Simulations and Experiments for Electrothermal-Chemical Guns Powered by Compulsators. IEEE Transaction on Magnetics,2003,39(1):427-439
[45]Shintate K, Sekine H. Numerical simulation of hypervelocity impact s of a projectile on laminated composite plate targets by means of improved SPH method[J]. Composites: A,2004,35:683-692.
[46]Petsehek A G, Libersky L D.Cylindral Smoothed Partiele Hydrodynamies.J ComPut Phys,1993,109:76-83
[47]金志明,宋明.火药床压缩模量及颗粒间应力.兵工学报,1990,1：28-35
[48]贝新源,岳宗五.三维SPH程序及其在斜高速碰撞问题的应用.计算物理,1997,14(2)：155-166
[49]龚凯,刘桦,王本龙.SPH固壁边界处理方法的改进.力学季刊,2008,29(4)：507-514
[50]郑坤,孙昭晨,张志明,周丰,赵西增.SPH数值模拟中边界处理方法及对比分析.水运工程,2009,8：23-27
[51]张刚明,王肖钧,王元博等.高速碰撞数值计算中的光滑粒子法.计算物理,2003,20(5)：447-454
[52]卞梁,王肖钧,章杰.高速碰撞数值计算中的SPH自适应粒子分布法.爆炸与冲击,2009,29(6)：607-612
[53]姚熊亮,陈娟,张阿漫,何江华.修正SPH方法在冲击波中的应用.哈尔滨工程大学学报,2010,31(1)：15-19
[54]刘东尧,郭海波,余永刚,周彦煌.毛细管消融等离子体及其射流压力特性研究.南京理工大学学报,2009,33(3)：348-370
[55]肖正刚,应三九,周伟良,徐复铭.低敏感高能发射药等离子体点火研究动态.含能材料,2008,16(5)：633-638
[56]狄加伟,杨敏涛,张明安,赵斌.电热化学发射技术在大口径火炮上的应用前景.火炮发射与控制学报,2010,(2)：24-27
[57]张军,邱沛蓉,董健年.电热化学炮脉冲形成网络分析及其参数设计.弹道学报,1997,9(1)：50-59
[58]翁春生,王浩.计算内弹道学.国防工业出版社,2006,1
[59]H.克里尔,M.萨默菲尔德.火炮内弹道.华东工程学院弹道研究所出版,1981
[60]金志明,袁亚雄.内弹道气动力原理.国防工业出版社,1983
[61]刘更,刘天祥,谢琴.无网格法及其应用.西北工业大学出版社,2005
[62]金志明,袁亚雄,宋明.现代内弹道学.北京理工大学,1992
[63]金志明.高速推进内弹道学.国防工业出版社,2001
[64]金志明,翁春生.高等内弹道学.高等教育出版社,2003
[65]金志明.枪炮内弹道学.北京理工大学出版社,2004
[66]刘大有.二相流体力学.
[67]周彦煌,王升晨.实用两相流内弹道学.第1版.兵器工业出版社,1990
[68]吴子牛.计算流体力学基本原理.科学出版社,2001
[69]董志勇.射流力学.科学出版社,2005
[70]韩旭,杨刚,强洪夫[译].光滑粒子流体动力学——一种无网格粒子法.湖南大学出版社,2005