复杂流场数值方法研究及在炮口制退器设计中应用
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摘要
枪炮发射时会形成复杂的膛口流场,炮口制退器的设计中需要对膛口流场特别是炮口制退器内部流场进行详细分析。不同复杂程度的膛口流场需要选用合适的算法进行模拟。
相对于整个后效期,弹丸飞离膛口的时间很短暂,如果不考虑运动弹丸的影响,膛口流场的数值模拟将得到很大简化。不带膛口装置或者带有锥形消焰器的膛口流场采用TVD有限体积法求解轴对称Euler方程进行模拟;对结构较简单的炮口制退器流场生成拼接的三维结构化网格,采用LU隐式因式分解方法和Jameson格式离散Euler方程求解;对于具有复杂结构的炮口制退器采用三维非结构网格和HLLC格式对火药气体排空过程进行数值模拟。
火炮发射过程中,弹丸和身管之间发生高速的相对滑动和分离,而分离的过程将导致流场拓扑结构的改变。针对三维流场拓扑结构的改变,对非结构重叠网格(OUG——Overset Unstructured grids)方法进行了改进。构造了确定非结构网格下洞边界的“曲面判定法”。叉树型数据结构具有很高的搜索效率,设计了“动态叉树”搜索算法用于“洞边界”(或网格间边界intergrid boundaries)上待插值点的贡献单元的搜索。解决了拓扑结构改变过程中重叠区域的建立和网格系之间流场信息的传递问题。采用OUG方法对弹丸与身管之间的高速滑动和分离过程进行了非定常数值模拟。
三维非定常流场的数值模拟带来巨大的计算量,并行计算技术是减少计算时间的有效工具,针对结构网格、非结构网格和OUG方法分别设计了三种并行算法。提出了基于多块拼接结构化网格的并行算法,建立了合理的网格分区策略,基于分区信息文件设计了通用的信息通信准则;由于非结构网格单元的空间分布具有很大灵活性,程序中采用单向链表对分区边界处的网格单元进行组织,建立了能适应任何分区拓扑结构的信息通讯准则;对于运动边界问题,随着流场中运动物体位置的改变,频繁进行网格的重新分区将耗费大量计算时间,针对OUG方法的特点设计了网格分区策略,不仅能避免网格分区的频繁重新划分,而且有利于提高重叠区中信息传递的效率,使程序得到简化的同时提高了其通用性。
以复杂流场的数值方法研究为基础,提出了新的炮口制退器设计计算方法。通过膛口流场的数值模拟获得后效期中带和不带炮口制退器时身管的受力变化曲线,计算身管的最大自由后坐速度,根据其物理定义计算炮口制退器的效率。针对某口径滑膛炮设计了一组炮口制退器,分别计算其效率并对各自冲击波场的发展过程进行分析。
本文建立了针对不同复杂程度膛口流场数值模拟的软件包。针对弹丸发射过程中流场拓扑结构的变化,对OUG方法进行了改进,并且有针对性地提出了高效的并行算法,可以有效地应用到航空、航天和兵器技术等领域的相关研究中。以复杂膛口流场数值模拟基础提出新的炮口制退器设计计算方法,将有助于新形势下火炮的整体设计。
Muzzle flow field formed after shooting is very complex. Detailed informations of a muzzle flow field, especially the flow field in the muzzle brake are necessary for designing the muzzle brake. Different methods are needed to simulate the flow field with different structures.
In the after-working period, projectile flies far from the the muzzle very fast. If the moving projectile is ignored, the simulation of muzzle flow field can be simplified greatly. Both of the muzzle flow fields with the action from a conical flame damper and without the action from any muzzle set are simulated using the TVD finite volume method to discrete the 2D axisymmetrical Euler equations. To simulate the flow field of the muzzle brake having simple structure, the Jameson difference scheme and the implicit LU factorization scheme are used to solve generalized Euler equations. Further more, the flow field with the action from a complex muzzle brake is simulated using unstructured grids and the HLLC scheme.
In a launching process, the relative sliding and departing takes place between a bullet and a barrel contacting with each other, and therefore topological structure of the flow field changes. An overset unstructured grid (OUG) method is proposed to simulate the changes of 3D flow field topological structure. A curved face criterion is proposed to define intergrid boundaries. The quadtree/octree search algorithm is efficient when used in the unstructured grids. A dynamic quadtree/octree search algorithm is proposed to search for donor cells of the nodes on the intergrid boundaries. The departure of the moving objects can cause persistent changes of flow field topological structure. The new OUG method can rebuild overset areas and transfer massages between subdomains in the departing process. The sliding and departing process between the bullet and the barrel is simulated by the OUG method.
It is a challenge to improve computing speed of simulating unsteady 3D flow field. However, the parallel computation technique is an effective tool to solve this problem. Three kinds of parallel algorithms are proposed for structured grids, unstructured grids and overset unstructured grids. In the parallel algorithm proposed for the structured grids, an effective domain partitioning method is proposed and a general communication criterion is accordingly proposed using the sub-domain information file. Because of the flexible spatial distribution of cells, the parallel algorithm of unstructured grids is more complex. In the program, unidirectional chained list is used to manage the cells located on the partition boundaries. The communication criterion based on the unstructured grids is available to simulate the flow fields with general sub-domain structures. If a moving object exists in the flow filed, it may cost much time to repartition the domain into sub-domains in the moving process of the object. To solve this problem, a special partitioning method is proposed according to the characteristic of the OUG method developed in this paper. Two kinds of message communications exist in using the parallel OUG method. One of them is the message communication on the partition boundaries, and the other one is that in the overlapped areas. By using the partitioning method proposed in the OUG method, the frequent repartitioning of the domain is avoided, and the efficiency of communications in the overlapped areas is improved.
A new method for designing muzzle brake is proposed based on the study of numerical method for simulating the complex muzzle flow fields. By recording the fluctuating force applied on the barrel, the maximum free backlash velocity of the barrel with or without the action from a muzzle brake can be calculated. Thus the efficiency of the muzzle brake can be obtained according to the definition. For the smooth bore artillery of a certain caliber, a series of muzzle brakes are designed according to different requirements. Further their efficiencies are calculated respectively, and the developing processes of the muzzle flow fields are also analyzed respectively.
A software package is built to simulate different muzzle flow fields. To simulate the changes of flow field topological structure, the OUG method is improved and a parallel algorithm is proposed for the OUG method. The parallel OUG method can be used in the studies of aeronautic, astronautic and weapon technology. A new method for designing a muzzle brake is proposed based on the simulation of complex muzzle flow field. This method is proved useful for promoting the design of the artillery.
相对于整个后效期,弹丸飞离膛口的时间很短暂,如果不考虑运动弹丸的影响,膛口流场的数值模拟将得到很大简化。不带膛口装置或者带有锥形消焰器的膛口流场采用TVD有限体积法求解轴对称Euler方程进行模拟;对结构较简单的炮口制退器流场生成拼接的三维结构化网格,采用LU隐式因式分解方法和Jameson格式离散Euler方程求解;对于具有复杂结构的炮口制退器采用三维非结构网格和HLLC格式对火药气体排空过程进行数值模拟。
火炮发射过程中,弹丸和身管之间发生高速的相对滑动和分离,而分离的过程将导致流场拓扑结构的改变。针对三维流场拓扑结构的改变,对非结构重叠网格(OUG——Overset Unstructured grids)方法进行了改进。构造了确定非结构网格下洞边界的“曲面判定法”。叉树型数据结构具有很高的搜索效率,设计了“动态叉树”搜索算法用于“洞边界”(或网格间边界intergrid boundaries)上待插值点的贡献单元的搜索。解决了拓扑结构改变过程中重叠区域的建立和网格系之间流场信息的传递问题。采用OUG方法对弹丸与身管之间的高速滑动和分离过程进行了非定常数值模拟。
三维非定常流场的数值模拟带来巨大的计算量,并行计算技术是减少计算时间的有效工具,针对结构网格、非结构网格和OUG方法分别设计了三种并行算法。提出了基于多块拼接结构化网格的并行算法,建立了合理的网格分区策略,基于分区信息文件设计了通用的信息通信准则;由于非结构网格单元的空间分布具有很大灵活性,程序中采用单向链表对分区边界处的网格单元进行组织,建立了能适应任何分区拓扑结构的信息通讯准则;对于运动边界问题,随着流场中运动物体位置的改变,频繁进行网格的重新分区将耗费大量计算时间,针对OUG方法的特点设计了网格分区策略,不仅能避免网格分区的频繁重新划分,而且有利于提高重叠区中信息传递的效率,使程序得到简化的同时提高了其通用性。
以复杂流场的数值方法研究为基础,提出了新的炮口制退器设计计算方法。通过膛口流场的数值模拟获得后效期中带和不带炮口制退器时身管的受力变化曲线,计算身管的最大自由后坐速度,根据其物理定义计算炮口制退器的效率。针对某口径滑膛炮设计了一组炮口制退器,分别计算其效率并对各自冲击波场的发展过程进行分析。
本文建立了针对不同复杂程度膛口流场数值模拟的软件包。针对弹丸发射过程中流场拓扑结构的变化,对OUG方法进行了改进,并且有针对性地提出了高效的并行算法,可以有效地应用到航空、航天和兵器技术等领域的相关研究中。以复杂膛口流场数值模拟基础提出新的炮口制退器设计计算方法,将有助于新形势下火炮的整体设计。
Muzzle flow field formed after shooting is very complex. Detailed informations of a muzzle flow field, especially the flow field in the muzzle brake are necessary for designing the muzzle brake. Different methods are needed to simulate the flow field with different structures.
In the after-working period, projectile flies far from the the muzzle very fast. If the moving projectile is ignored, the simulation of muzzle flow field can be simplified greatly. Both of the muzzle flow fields with the action from a conical flame damper and without the action from any muzzle set are simulated using the TVD finite volume method to discrete the 2D axisymmetrical Euler equations. To simulate the flow field of the muzzle brake having simple structure, the Jameson difference scheme and the implicit LU factorization scheme are used to solve generalized Euler equations. Further more, the flow field with the action from a complex muzzle brake is simulated using unstructured grids and the HLLC scheme.
In a launching process, the relative sliding and departing takes place between a bullet and a barrel contacting with each other, and therefore topological structure of the flow field changes. An overset unstructured grid (OUG) method is proposed to simulate the changes of 3D flow field topological structure. A curved face criterion is proposed to define intergrid boundaries. The quadtree/octree search algorithm is efficient when used in the unstructured grids. A dynamic quadtree/octree search algorithm is proposed to search for donor cells of the nodes on the intergrid boundaries. The departure of the moving objects can cause persistent changes of flow field topological structure. The new OUG method can rebuild overset areas and transfer massages between subdomains in the departing process. The sliding and departing process between the bullet and the barrel is simulated by the OUG method.
It is a challenge to improve computing speed of simulating unsteady 3D flow field. However, the parallel computation technique is an effective tool to solve this problem. Three kinds of parallel algorithms are proposed for structured grids, unstructured grids and overset unstructured grids. In the parallel algorithm proposed for the structured grids, an effective domain partitioning method is proposed and a general communication criterion is accordingly proposed using the sub-domain information file. Because of the flexible spatial distribution of cells, the parallel algorithm of unstructured grids is more complex. In the program, unidirectional chained list is used to manage the cells located on the partition boundaries. The communication criterion based on the unstructured grids is available to simulate the flow fields with general sub-domain structures. If a moving object exists in the flow filed, it may cost much time to repartition the domain into sub-domains in the moving process of the object. To solve this problem, a special partitioning method is proposed according to the characteristic of the OUG method developed in this paper. Two kinds of message communications exist in using the parallel OUG method. One of them is the message communication on the partition boundaries, and the other one is that in the overlapped areas. By using the partitioning method proposed in the OUG method, the frequent repartitioning of the domain is avoided, and the efficiency of communications in the overlapped areas is improved.
A new method for designing muzzle brake is proposed based on the study of numerical method for simulating the complex muzzle flow fields. By recording the fluctuating force applied on the barrel, the maximum free backlash velocity of the barrel with or without the action from a muzzle brake can be calculated. Thus the efficiency of the muzzle brake can be obtained according to the definition. For the smooth bore artillery of a certain caliber, a series of muzzle brakes are designed according to different requirements. Further their efficiencies are calculated respectively, and the developing processes of the muzzle flow fields are also analyzed respectively.
A software package is built to simulate different muzzle flow fields. To simulate the changes of flow field topological structure, the OUG method is improved and a parallel algorithm is proposed for the OUG method. The parallel OUG method can be used in the studies of aeronautic, astronautic and weapon technology. A new method for designing a muzzle brake is proposed based on the simulation of complex muzzle flow field. This method is proved useful for promoting the design of the artillery.
引文
[1]尤国钊,许厚谦,杨启仁.中间弹道学.北京:国防工业出版社,2003,1:3
[2]傅德薰,汪翼云,马延文.计算空气动力学.北京:宇航出版社,1994
[3]Harten A.High resolution for hyperbolic conservation laws.J Comput Phys.,1983,49:357-393
[4]刘儒勋,舒其望.计算流体力学的若干新方法,北京:科学出版社,2004:77
[5]刘希云,赵润祥.流体力学中的有限元与边界元方法.上海:上海交通大学出版社,1992
[6]Lucy L.B.A numerical approach to the testing of the fission hypothesis.Astronomical Journal,1977,82(12):1013-24
[7]Belytschko T,Organ D.Krongauz Y.Coupled finite element-element-free Galerkin method.Computational Mechanics,1995,17(3):186-195
[8]Welterlen T J,Karman S L.Rapid assessment of F-16 store trajectories using unstructured CFD.AIAA,1995,95-0354
[9]Parikh Paresh,Pirzadeh Shahyar,Frink Neal T.Unstructured grid solution to a wing/pylon/store configuration.Journal of Aircraft,1994,31(6):1291-1296
[10]Tomaro R F,Witzenman F C,Strang W Z.Simulation of store separation for the F/A-18C using cobalt_(60).Journal of Aircraft,2000,37(3):361-367
[11]Welterlen Tracy J,Leone Chris.Application of viscous,Cartesian CFD to aircraft stores carriage and separation simulation.AIAA,1996,96-2453
[12]Gillyboeuf J P,Mansuy P,Pavsic S.Two new chimera methods - Application to missile separation.AIAA,1995,95-0353
[13]Zhong Xiaolin,Shen Jian W.An efficient semi-implicit time accurate scheme for unsteady viscous flow on dynamic grids.AIAA,1997,97-0726
[14]杨爱民,乔志德.基于运动嵌套网格的前飞翼绕流N-S方程数值计算.航空学报,2001,22(5):434-436
[15]李孝伟,范绪箕.基于嵌套网格的飞行器外挂物投放的数值模拟.空气动力学学报,2004,22(1):114-117
[16]招启军,徐国华.基于嵌套网格和计入尾迹影响的旋翼流场数值模拟.南京航空航天大学学报,2005,37(6):675-679
[17]Jones William T,Samareh Abolhassani Jamshid.A grid generation system for multi-disciplinary design optimization.AIAA,1995,95-1689
[18]Robinson Brian A,Batina John T,Yang Henry T Y.Aeroelastic analysis of wings using the Euler equations with a deforming mesh.Journal of Aircraft,1991,28(11):781-788
[19]Reuther J,Rimlinger M J,Alonso J J.Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers.AIAA,1996,96-4045
[20]Gaitonde Ann L,Fiddes S P A.Moving mesh system for the calculation of unsteady flows.AIAA,1996,93-0641
[21]Rumsey Christopher L,Anderson W Kyle.Some numerical and physical aspects of unsteady Navier-Stokes computations over airfoils using dynamic meshes.AIAA,1988,88-0329
[22]Batina J.Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes.AIAA Journal,1990,29(11):1836-1843
[23]Formggia L,Peraire J,Morgan K.Simulation of a store separation using the finite element method.Applied Mathematical Modelling,1988,12(2):175-181
[25]Farhat C,Degand C,Koobus B,Lesoinne M.Torsional springs for two-dimensional dynamic unstructured fluid meshes.Computer Methods in Applied Mechanics and Engineering,1998,163(1-4):231-245
[25]郭正.包含运动边界的多体非定常流场数值模拟方法研究.国防科技大学博士论文,2002
[26]Batina J T.Unsteady Euler airfoil solutions using unstructured dynamic meshes.AIAA Journal,1990,28(8):1381-1388
[27]Blom F J.Considerations on the spring analogy.International Journal for Numerical Methods in Fluids,2000,32(6):647-668
[28]Tezduyar T E,Behr M,Mittal S,Liou J.New strategy for finite element computations involving moving boundaries and interfaces.The deforming-spatial-domain/space-time procedure.Ⅰ.The concept and the preliminary numerical tests.Computer Methods in Applied Mechanics and Engineering,1992,94(3):339-351
[29]Tezduyar T E,Behr M,Mittal S,Liou J.New strategy for finite element computations involving moving boundaries and interfaces.The deforming/spatial-domain/space-time procedure.Ⅱ.Computation of free-surface flows,two-liquid flows,and flows with drifting cylinders.Computer Methods in Applied Mechanics and Engineering,1992,94(3):353-371
[30]Tezduyar Tayfum,Aliabadi Sbabrouz,Behr Marek.Parallel finite-element computation of 3D flows.Computer.1993,26(10):27-36
[31]Johnson A A,Tezduyar T E.Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces.Computer Methods in Applied Mechanics and Engineering,1994,119(1-2):73-94
[32]Johnson A A,Tezduyar T E.Simulation of multiple spheres falling in a liquid-filled tube.Computer Methods in Applied Mechanics and Engineering,1996,134(3-4):351-357
[33]Behr M,Tezduyar T.The shear-slip mesh update method.Computer Methods in Applied Mechanics and Engineering,1999,174(3-4):261-274
[34]Cavallo Peter A,Hosangadi Ashvin,Lee Robert A.Dynamic unstructured grid methodologywith application to aero/propulsive flowfields.AIAA,1997,97-2310
[35]Baker Timothy J,Cavallo Peter A.Dynamic adaptation for deforming tetrahedral meshes.AIAA,1999,99-3253
[36]Nielsen Eric J,Anderson W Kyle.Recent improvements in aerodynamic design optimization on unstructured meshes.AIAA,2001,2001-0596
[37]Baker T J.Mesh movement and metamorphosis.Engineering with Computers,2002,18(3):188-198
[38]Cavallo Peter,Sinha Neeraj,Feldman Gregory.Parallel unstructured mesh adaptation for transient moving body and aeropropulsive applications.AIAA,2004,2004-1057
[39]Stein K,Tezduyar T,Benney R.Mesh moving techniques for fluid-structure interactions with large displacements.Journal of Applied Mechanics,2003,70(1):58-63
[40]Stein Keith,Tezduyar Tayfun E,Benney Richard.Automatic mesh update with the solid-extension mesh moving technique.Computer Methods in Applied Mechanics and Engineering,2004,193(21-22):2019-2032
[41]Baum Joseph D,Luo Hong,Loehner Rainald.A new ALE adaptive unstructured methodology for the simulation of moving bodies.AIAA,1994,94-0414
[42]Formaggia L,Peraire J,Morgan K.Simulation of a store separation using the finite element method.Applied Mathematical Modelling,1988,12(2):175-181
[43]Lohner Rainald.Adaptive remeshing for transient problems.Computer Methods in Applied Mechanics and Engineering,1989,75(1-3):195-214
[44]Lohner Rainald,Baum Joseph D.Three-dimensional store separation using a finite element solver and adaptive remeshing.AIAA,1991,91-0602
[45]张军,耿继辉,谭俊杰.用HLLC方法处理运动边界.力学与实践,2004,26(2):21-24
[46]张军,耿继辉,谭俊杰.三维非结构运动网格的生成.弹道学报,2004,16(1):43-46
[47]谭俊杰,张军,耿继辉.激波诱导圆柱运动数值模拟南京理工大学学报,2003,27(5):578-582
[48]张军,谭俊杰,任登凤.副油箱从机翼分离流场数值模拟.自然科学进展,2006,16(8): 1033-1037
[49]张军,谭俊杰,褚江.一种新的非结构动网格生成方法.南京航空航天大学学报,2007,39(5):633-636
[50]Baum Joseph D,Loehner Rainald.Numerical simulation of pilot/seat ejection from an F-16.AIAA,1993,93-0783
[51]Baum Joseph D,Luo Hong,Loehner Rainald.Application of unstructured adaptive moving body methodology to the simulation of fuel tank separation from an F-16 fighter.AIAA,1997,97-0166
[52]Steger Joseph L,Dougherty F Carroll,Benek John A.Chimera grid scheme.American Society of Mechanical Engineers,Fluids Engineering Division,1983,5:59-69
[53]Kazuhiro Nakahashi,Fumiya Togashi.An intergrid-boundary definition method for overset unstructured grid approach.AIAA,1999,99-3304
[54]Fumiya Togashi,Kazuhiro Nakahashi,Yasushi Ito.Flow simulation of NAL experimental supersonic airplane/booster separation using overset unstructured grids.AIAA,2000,2000-1007
[55]Fumiya Togashi,Yasushi Ito.Flow simulation of flapping wings of an insect using overset unstructured grid.AIAA,2001,2001-2619
[56]Fumiya Togashi,Yasushi Ito,Kazuhiro Nakahashi:Extension of overset unstructured grids to multiple bodies in contact.AIAA,2002,2002-2809
[57]蒋光南.三维重叠网格生成技术.民用飞机设计与研究,1995,1:15-22
[58]Loehner Rainald,Sharov Dmitri,Luo Hong.Overlapping unstructured grids.AIAA,2001,2001-0439
[59]田书玲,伍贻兆,夏健.基于非结构重叠网格的二维外挂物投放模拟.空气动力学学报,2007,25(2):245-249
[60]田书玲,伍贻兆,夏健.用动态非结构重叠网格法模拟三维多体相对运动绕流.航空学报,2007,28(1):46-51
[61]Luo Hong,Sharov Dmitri,Baum Joseph D.An overlapping unstructured grid method for viscous flows.AIAA,2001,2001-2603
[62]Togashi Fumiya,Ito Yasushi,Nakahashi Kazuhiro.Overset unstructured grids method for viscous flow computations.AIAA Journal,2006,44(7):1617-1623
[63]Zhang S J,Liu J,Chen Y S.Numerical simulation of stage separation with an unstructured chimera grid method.AIAA,2004,2004-4723
[64]Zhang S J,Liu J,Chen Y S.An unstructured chimera grid method for moving geometries.AIAA,2005,2005-0323
[65]张月林等.火炮反后坐装置设计.北京:国防工业出版社,1984,255-304
[66]Salsbury M J.The effects of a muzzle brake's diameter and length on overpressure and efficiency.U.S Army Weapons Command,Rock Island Arsenal.IL.October 1966,TR 66-2920.
[67]Pater L L.Muzzle brake parameter study.Naval Surface Weapons Center,Danlgren,VA,October 1976,TR-3531
[68]Schmidt E M,Gion E.J.,Fansler K.S.Measurement of muzzle blast and its impingement upon surfaces.AIAA,1979,79-150
[69]Abbett M.The roach disc in the underexpanded exhausted plume.AIAA,1970,70-231
[70]Dash S M,Wolf D E.Interactive Phenomena in Supersonic Jet Mixing Problems.AIAA,1983,A83-16826(AH)
[71]Jiang Z,Takayama K,Skews B W.Wave interactions following the emergence of a supersonic projectile from a tube.17th International Symposium on Ballistic,1998,LD002
[72]Zonglin Jiang,Yonghui Huang,Kazuyoshi Takayama.Shocked flows induced by supersonic projectiles moving in tubes.Computers and Fluid,2004,33(7):953-966
[73]Sakamoto K,Matsunnaga K,Fukushima J,Tanaka A.Numerical anaysis of the propagating blast wave in a firing range.19th International Symposium on Ballistic,2001,LD10
[74]Zibarov A V,Babayev D B,Mironov A A.Numerical simulation of 3d muzzle brake and missile launcher flow field in the presence of movable objects.20th International Symposium on Ballistic,2002,225-232
[75]Zibarov A V,Babayev D B,Konstantinov P V.Numerical simulation of the finned projectile pass through two chamber muzzle brake.21st International Symposium on Ballistic,2004:1288-1295
[76]Roxan Cayzac,Eric Carette,Thierry Alziary de Roquefort.Unsteady intermediate ballistics:2D and 3D modeling,application to sabot separation.22nd International Symposium on Ballistic,2005:398-405
[77]Cayzac R,Carette E,T A de Roquefort.3D unsteady intermediate ballistic modeling:muzzle brake and sabot separation.24th International Symposium on Ballistic,2008:399-405
[78]李鸿志,尤国钊.炮口冲击波的形成和分布规律以及对减小冲击波途径的分析.华东工程学院学报,1977,1:26-48
[79]李鸿志,高树滋.带膛口装置的膛口流场与冲击波形成机理.华东工程学院学报,1982,3:1-26
[80]马大为.含复杂波系的膛口非定常流场的数值模拟.南京理工大学博士论文,1991
[81]乐贵高,马大为,冯勇.某火炮膛口流场数值仿真.兵工学报,2004,25(1):19-22
[82]江坤,钱林方.某火炮炮口制退器的研究.弹道学报,2006,18(3):55-57
[83]杨勇.火箭发射系统冲击流场TVD有限体积法数值模拟及工程应用.南京理工大学博士论文,1996:30-38
[84]Yee H C,Warming R F,Harten A.Implicit total variation diminishing(TVD) schemes for steady-state calculations.21st American Institute of Aeronautics and Astronautics,Aerospace Sciences Meeting,Reno,NV,United States,1983,23
[85]Wang J C T,Widhopf G F.Numerical simulation of blast flowfields using a high resolution TVD finite volume scheme.AIAA,1987:87-1320
[86]张月林等.火炮反后坐装置设计.北京:国防工业出版社,1984:25
[87]李鸿志,崔东明,范宝春.连续介质中的激波.北京:兵器工业出版社,1995:58
[88]茅泉美.底部排气弹燃烧特性研究与数值分析.南京理工大学硕士论文,2006
[89]陈民生.试论影响火药气体常数的诸因素.南京理工大学学报,1978,2:20-28
[90]崔龙波.有和没有底部排气时绕弹丸三维流场的数值模拟.南京理工大学硕士论文,1998
[91]张涵信,沈孟育.计算流体力学——差分方法的原理与应用.北京:国防工业出版社,2003:306-312
[92]陈国良,吴俊敏.并行计算机体系结构.北京:高等教育出版社,2002:32-42
[93]Harten A,Lax P D,Van Leer B.On upstream differencing and Godunov-Type schemes for hyperbolic conservation laws.SIAM Review,1983,25(1):35-61
[94]Toro E F.Riemann solvers and numerical methods for fluid dynamics(chapter 10),springer,Berlin,1997
[95]Batten P,Leschziner M A,Goldberg U C.Average-State jacobians and implicit methods for compressible viscous and turbulent flows.Journal of Computational Physics,1997,137(1):38-78
[96]Sun M,Takayama K.An artificially upstream flux vector splitting scheme for the Euler equations.Journal of Computational Physics,2003,189(1):305-329
[97]牛俊强,杨振虎.混合网格并行计算的分区方法.弹箭与制导学报,2006,5:233-236
[98]Sod G.A.A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws.Journal of Computational Physics,1978,27(1):1-31
[99]张震霖,外挂物投放技术的数值方法研究,西北工业大学硕士学位论文,2004
[100]L(o|¨)hner R.Robust,vectorized search algorithms for interpolation on unstructured grids.Journal of Computational Physics,1995,118(2):380-387
[101]Marshall C Galbraith.Development and application of a general interpolation algorithm.AIAA,2006,2006-3851
[102]Burkardt J."GEOMETRY Geometric Calculations," FSU Computational Sciences Faculty Web Page,URL:http://www.csit.fsu.edu/～burkardt/f_src/geometry/geometry,html [cited 28 June 2005]
[103]L(o|¨)hner Rainald.Some useful data structures for the generation of unstructured grids.Communications in Applied Numerical Methods.1988,4(1):123-135
[104]Samet H.The quadtree and related hierarchical data structures.Computing Surveys,1984,16(2):187-260
[105]Bonet Javier,Peraire Jaime.Alternating digital tree(ADT) algorithm for 3D geometric searching and intersection problems.International Journal for Numerical Methods in Engineering,1991,31(1):1-17
[106]Merlen A,Dyment A.Similarity and asymptotic analysis for gun-firing aerodynamics.J.Fluid Mech.,1991,225:497-528
[107]邱凤昌,张月林.炮口装置.北京:国防工业出版社,1974
[2]傅德薰,汪翼云,马延文.计算空气动力学.北京:宇航出版社,1994
[3]Harten A.High resolution for hyperbolic conservation laws.J Comput Phys.,1983,49:357-393
[4]刘儒勋,舒其望.计算流体力学的若干新方法,北京:科学出版社,2004:77
[5]刘希云,赵润祥.流体力学中的有限元与边界元方法.上海:上海交通大学出版社,1992
[6]Lucy L.B.A numerical approach to the testing of the fission hypothesis.Astronomical Journal,1977,82(12):1013-24
[7]Belytschko T,Organ D.Krongauz Y.Coupled finite element-element-free Galerkin method.Computational Mechanics,1995,17(3):186-195
[8]Welterlen T J,Karman S L.Rapid assessment of F-16 store trajectories using unstructured CFD.AIAA,1995,95-0354
[9]Parikh Paresh,Pirzadeh Shahyar,Frink Neal T.Unstructured grid solution to a wing/pylon/store configuration.Journal of Aircraft,1994,31(6):1291-1296
[10]Tomaro R F,Witzenman F C,Strang W Z.Simulation of store separation for the F/A-18C using cobalt_(60).Journal of Aircraft,2000,37(3):361-367
[11]Welterlen Tracy J,Leone Chris.Application of viscous,Cartesian CFD to aircraft stores carriage and separation simulation.AIAA,1996,96-2453
[12]Gillyboeuf J P,Mansuy P,Pavsic S.Two new chimera methods - Application to missile separation.AIAA,1995,95-0353
[13]Zhong Xiaolin,Shen Jian W.An efficient semi-implicit time accurate scheme for unsteady viscous flow on dynamic grids.AIAA,1997,97-0726
[14]杨爱民,乔志德.基于运动嵌套网格的前飞翼绕流N-S方程数值计算.航空学报,2001,22(5):434-436
[15]李孝伟,范绪箕.基于嵌套网格的飞行器外挂物投放的数值模拟.空气动力学学报,2004,22(1):114-117
[16]招启军,徐国华.基于嵌套网格和计入尾迹影响的旋翼流场数值模拟.南京航空航天大学学报,2005,37(6):675-679
[17]Jones William T,Samareh Abolhassani Jamshid.A grid generation system for multi-disciplinary design optimization.AIAA,1995,95-1689
[18]Robinson Brian A,Batina John T,Yang Henry T Y.Aeroelastic analysis of wings using the Euler equations with a deforming mesh.Journal of Aircraft,1991,28(11):781-788
[19]Reuther J,Rimlinger M J,Alonso J J.Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers.AIAA,1996,96-4045
[20]Gaitonde Ann L,Fiddes S P A.Moving mesh system for the calculation of unsteady flows.AIAA,1996,93-0641
[21]Rumsey Christopher L,Anderson W Kyle.Some numerical and physical aspects of unsteady Navier-Stokes computations over airfoils using dynamic meshes.AIAA,1988,88-0329
[22]Batina J.Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes.AIAA Journal,1990,29(11):1836-1843
[23]Formggia L,Peraire J,Morgan K.Simulation of a store separation using the finite element method.Applied Mathematical Modelling,1988,12(2):175-181
[25]Farhat C,Degand C,Koobus B,Lesoinne M.Torsional springs for two-dimensional dynamic unstructured fluid meshes.Computer Methods in Applied Mechanics and Engineering,1998,163(1-4):231-245
[25]郭正.包含运动边界的多体非定常流场数值模拟方法研究.国防科技大学博士论文,2002
[26]Batina J T.Unsteady Euler airfoil solutions using unstructured dynamic meshes.AIAA Journal,1990,28(8):1381-1388
[27]Blom F J.Considerations on the spring analogy.International Journal for Numerical Methods in Fluids,2000,32(6):647-668
[28]Tezduyar T E,Behr M,Mittal S,Liou J.New strategy for finite element computations involving moving boundaries and interfaces.The deforming-spatial-domain/space-time procedure.Ⅰ.The concept and the preliminary numerical tests.Computer Methods in Applied Mechanics and Engineering,1992,94(3):339-351
[29]Tezduyar T E,Behr M,Mittal S,Liou J.New strategy for finite element computations involving moving boundaries and interfaces.The deforming/spatial-domain/space-time procedure.Ⅱ.Computation of free-surface flows,two-liquid flows,and flows with drifting cylinders.Computer Methods in Applied Mechanics and Engineering,1992,94(3):353-371
[30]Tezduyar Tayfum,Aliabadi Sbabrouz,Behr Marek.Parallel finite-element computation of 3D flows.Computer.1993,26(10):27-36
[31]Johnson A A,Tezduyar T E.Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces.Computer Methods in Applied Mechanics and Engineering,1994,119(1-2):73-94
[32]Johnson A A,Tezduyar T E.Simulation of multiple spheres falling in a liquid-filled tube.Computer Methods in Applied Mechanics and Engineering,1996,134(3-4):351-357
[33]Behr M,Tezduyar T.The shear-slip mesh update method.Computer Methods in Applied Mechanics and Engineering,1999,174(3-4):261-274
[34]Cavallo Peter A,Hosangadi Ashvin,Lee Robert A.Dynamic unstructured grid methodologywith application to aero/propulsive flowfields.AIAA,1997,97-2310
[35]Baker Timothy J,Cavallo Peter A.Dynamic adaptation for deforming tetrahedral meshes.AIAA,1999,99-3253
[36]Nielsen Eric J,Anderson W Kyle.Recent improvements in aerodynamic design optimization on unstructured meshes.AIAA,2001,2001-0596
[37]Baker T J.Mesh movement and metamorphosis.Engineering with Computers,2002,18(3):188-198
[38]Cavallo Peter,Sinha Neeraj,Feldman Gregory.Parallel unstructured mesh adaptation for transient moving body and aeropropulsive applications.AIAA,2004,2004-1057
[39]Stein K,Tezduyar T,Benney R.Mesh moving techniques for fluid-structure interactions with large displacements.Journal of Applied Mechanics,2003,70(1):58-63
[40]Stein Keith,Tezduyar Tayfun E,Benney Richard.Automatic mesh update with the solid-extension mesh moving technique.Computer Methods in Applied Mechanics and Engineering,2004,193(21-22):2019-2032
[41]Baum Joseph D,Luo Hong,Loehner Rainald.A new ALE adaptive unstructured methodology for the simulation of moving bodies.AIAA,1994,94-0414
[42]Formaggia L,Peraire J,Morgan K.Simulation of a store separation using the finite element method.Applied Mathematical Modelling,1988,12(2):175-181
[43]Lohner Rainald.Adaptive remeshing for transient problems.Computer Methods in Applied Mechanics and Engineering,1989,75(1-3):195-214
[44]Lohner Rainald,Baum Joseph D.Three-dimensional store separation using a finite element solver and adaptive remeshing.AIAA,1991,91-0602
[45]张军,耿继辉,谭俊杰.用HLLC方法处理运动边界.力学与实践,2004,26(2):21-24
[46]张军,耿继辉,谭俊杰.三维非结构运动网格的生成.弹道学报,2004,16(1):43-46
[47]谭俊杰,张军,耿继辉.激波诱导圆柱运动数值模拟南京理工大学学报,2003,27(5):578-582
[48]张军,谭俊杰,任登凤.副油箱从机翼分离流场数值模拟.自然科学进展,2006,16(8): 1033-1037
[49]张军,谭俊杰,褚江.一种新的非结构动网格生成方法.南京航空航天大学学报,2007,39(5):633-636
[50]Baum Joseph D,Loehner Rainald.Numerical simulation of pilot/seat ejection from an F-16.AIAA,1993,93-0783
[51]Baum Joseph D,Luo Hong,Loehner Rainald.Application of unstructured adaptive moving body methodology to the simulation of fuel tank separation from an F-16 fighter.AIAA,1997,97-0166
[52]Steger Joseph L,Dougherty F Carroll,Benek John A.Chimera grid scheme.American Society of Mechanical Engineers,Fluids Engineering Division,1983,5:59-69
[53]Kazuhiro Nakahashi,Fumiya Togashi.An intergrid-boundary definition method for overset unstructured grid approach.AIAA,1999,99-3304
[54]Fumiya Togashi,Kazuhiro Nakahashi,Yasushi Ito.Flow simulation of NAL experimental supersonic airplane/booster separation using overset unstructured grids.AIAA,2000,2000-1007
[55]Fumiya Togashi,Yasushi Ito.Flow simulation of flapping wings of an insect using overset unstructured grid.AIAA,2001,2001-2619
[56]Fumiya Togashi,Yasushi Ito,Kazuhiro Nakahashi:Extension of overset unstructured grids to multiple bodies in contact.AIAA,2002,2002-2809
[57]蒋光南.三维重叠网格生成技术.民用飞机设计与研究,1995,1:15-22
[58]Loehner Rainald,Sharov Dmitri,Luo Hong.Overlapping unstructured grids.AIAA,2001,2001-0439
[59]田书玲,伍贻兆,夏健.基于非结构重叠网格的二维外挂物投放模拟.空气动力学学报,2007,25(2):245-249
[60]田书玲,伍贻兆,夏健.用动态非结构重叠网格法模拟三维多体相对运动绕流.航空学报,2007,28(1):46-51
[61]Luo Hong,Sharov Dmitri,Baum Joseph D.An overlapping unstructured grid method for viscous flows.AIAA,2001,2001-2603
[62]Togashi Fumiya,Ito Yasushi,Nakahashi Kazuhiro.Overset unstructured grids method for viscous flow computations.AIAA Journal,2006,44(7):1617-1623
[63]Zhang S J,Liu J,Chen Y S.Numerical simulation of stage separation with an unstructured chimera grid method.AIAA,2004,2004-4723
[64]Zhang S J,Liu J,Chen Y S.An unstructured chimera grid method for moving geometries.AIAA,2005,2005-0323
[65]张月林等.火炮反后坐装置设计.北京:国防工业出版社,1984,255-304
[66]Salsbury M J.The effects of a muzzle brake's diameter and length on overpressure and efficiency.U.S Army Weapons Command,Rock Island Arsenal.IL.October 1966,TR 66-2920.
[67]Pater L L.Muzzle brake parameter study.Naval Surface Weapons Center,Danlgren,VA,October 1976,TR-3531
[68]Schmidt E M,Gion E.J.,Fansler K.S.Measurement of muzzle blast and its impingement upon surfaces.AIAA,1979,79-150
[69]Abbett M.The roach disc in the underexpanded exhausted plume.AIAA,1970,70-231
[70]Dash S M,Wolf D E.Interactive Phenomena in Supersonic Jet Mixing Problems.AIAA,1983,A83-16826(AH)
[71]Jiang Z,Takayama K,Skews B W.Wave interactions following the emergence of a supersonic projectile from a tube.17th International Symposium on Ballistic,1998,LD002
[72]Zonglin Jiang,Yonghui Huang,Kazuyoshi Takayama.Shocked flows induced by supersonic projectiles moving in tubes.Computers and Fluid,2004,33(7):953-966
[73]Sakamoto K,Matsunnaga K,Fukushima J,Tanaka A.Numerical anaysis of the propagating blast wave in a firing range.19th International Symposium on Ballistic,2001,LD10
[74]Zibarov A V,Babayev D B,Mironov A A.Numerical simulation of 3d muzzle brake and missile launcher flow field in the presence of movable objects.20th International Symposium on Ballistic,2002,225-232
[75]Zibarov A V,Babayev D B,Konstantinov P V.Numerical simulation of the finned projectile pass through two chamber muzzle brake.21st International Symposium on Ballistic,2004:1288-1295
[76]Roxan Cayzac,Eric Carette,Thierry Alziary de Roquefort.Unsteady intermediate ballistics:2D and 3D modeling,application to sabot separation.22nd International Symposium on Ballistic,2005:398-405
[77]Cayzac R,Carette E,T A de Roquefort.3D unsteady intermediate ballistic modeling:muzzle brake and sabot separation.24th International Symposium on Ballistic,2008:399-405
[78]李鸿志,尤国钊.炮口冲击波的形成和分布规律以及对减小冲击波途径的分析.华东工程学院学报,1977,1:26-48
[79]李鸿志,高树滋.带膛口装置的膛口流场与冲击波形成机理.华东工程学院学报,1982,3:1-26
[80]马大为.含复杂波系的膛口非定常流场的数值模拟.南京理工大学博士论文,1991
[81]乐贵高,马大为,冯勇.某火炮膛口流场数值仿真.兵工学报,2004,25(1):19-22
[82]江坤,钱林方.某火炮炮口制退器的研究.弹道学报,2006,18(3):55-57
[83]杨勇.火箭发射系统冲击流场TVD有限体积法数值模拟及工程应用.南京理工大学博士论文,1996:30-38
[84]Yee H C,Warming R F,Harten A.Implicit total variation diminishing(TVD) schemes for steady-state calculations.21st American Institute of Aeronautics and Astronautics,Aerospace Sciences Meeting,Reno,NV,United States,1983,23
[85]Wang J C T,Widhopf G F.Numerical simulation of blast flowfields using a high resolution TVD finite volume scheme.AIAA,1987:87-1320
[86]张月林等.火炮反后坐装置设计.北京:国防工业出版社,1984:25
[87]李鸿志,崔东明,范宝春.连续介质中的激波.北京:兵器工业出版社,1995:58
[88]茅泉美.底部排气弹燃烧特性研究与数值分析.南京理工大学硕士论文,2006
[89]陈民生.试论影响火药气体常数的诸因素.南京理工大学学报,1978,2:20-28
[90]崔龙波.有和没有底部排气时绕弹丸三维流场的数值模拟.南京理工大学硕士论文,1998
[91]张涵信,沈孟育.计算流体力学——差分方法的原理与应用.北京:国防工业出版社,2003:306-312
[92]陈国良,吴俊敏.并行计算机体系结构.北京:高等教育出版社,2002:32-42
[93]Harten A,Lax P D,Van Leer B.On upstream differencing and Godunov-Type schemes for hyperbolic conservation laws.SIAM Review,1983,25(1):35-61
[94]Toro E F.Riemann solvers and numerical methods for fluid dynamics(chapter 10),springer,Berlin,1997
[95]Batten P,Leschziner M A,Goldberg U C.Average-State jacobians and implicit methods for compressible viscous and turbulent flows.Journal of Computational Physics,1997,137(1):38-78
[96]Sun M,Takayama K.An artificially upstream flux vector splitting scheme for the Euler equations.Journal of Computational Physics,2003,189(1):305-329
[97]牛俊强,杨振虎.混合网格并行计算的分区方法.弹箭与制导学报,2006,5:233-236
[98]Sod G.A.A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws.Journal of Computational Physics,1978,27(1):1-31
[99]张震霖,外挂物投放技术的数值方法研究,西北工业大学硕士学位论文,2004
[100]L(o|¨)hner R.Robust,vectorized search algorithms for interpolation on unstructured grids.Journal of Computational Physics,1995,118(2):380-387
[101]Marshall C Galbraith.Development and application of a general interpolation algorithm.AIAA,2006,2006-3851
[102]Burkardt J."GEOMETRY Geometric Calculations," FSU Computational Sciences Faculty Web Page,URL:http://www.csit.fsu.edu/～burkardt/f_src/geometry/geometry,html [cited 28 June 2005]
[103]L(o|¨)hner Rainald.Some useful data structures for the generation of unstructured grids.Communications in Applied Numerical Methods.1988,4(1):123-135
[104]Samet H.The quadtree and related hierarchical data structures.Computing Surveys,1984,16(2):187-260
[105]Bonet Javier,Peraire Jaime.Alternating digital tree(ADT) algorithm for 3D geometric searching and intersection problems.International Journal for Numerical Methods in Engineering,1991,31(1):1-17
[106]Merlen A,Dyment A.Similarity and asymptotic analysis for gun-firing aerodynamics.J.Fluid Mech.,1991,225:497-528
[107]邱凤昌,张月林.炮口装置.北京:国防工业出版社,1974