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王宁等:基于无网格伽辽金法的连铸坯凝固计算方法 ·193· 布置非均匀网格时网格过渡区域复杂的数据传 [8]Yamasaki N.Shima S.Tsunenari K.et al.Particle-based numerical 递,在非规则随机节点设置方面显示出极大的灵 analysis of spray water flow in secondary cooling of continuous 活性 casting machines.ISI/Int,2015,55(5):976 [9] Vaghefi R,Hematiyan M R,Nayebi A.Three-dimensional thermo- (3)相比于有限元基于网格的数值模拟方法, elastoplastic analysis of thick functionally graded plates using the EFG法回避了网格依赖性,具有良好的精度和自 meshless local Petrov -Galerkin method.Eng Anal Boundary 适应性,为进一步探索坯壳重构、液固界面追踪、 Elem,2016,71:34 裂纹形成等网格模拟方法难以甚至无法处理的问 [10]Hostos J C A,Bencomo A D,Cabrera E S P.Simple iterative 题,提供了高效、可行的数值计算方法 procedure for the thermal-mechanical analysis of continuous casting processes using the element-free Galerkin method.J Therm 参考文献 Stresses,2018,41(2):160 [11]Hu P H,Wang X D,Wei JJ,et al.Investigation of liquid/solid slag [1]Jing D J,Cai KK.Numerical simulation of the coupling and air gap behavior inside the mold during continuous slab phenomenon between thermal and mechanical fields of billet in casting.ISI/Int,2018,58(5):892 continuous casting mold.JUniv SciTechnol Beijing,2000,22(5): [12]Fan Y H.A Study of Meshless Method in Numerical Heat 417 Transfer[Dissertation].Nanjing:Nanjing University of Science (荆德君,蔡开科.连铸结品器内铸坯温度场和应力场耦合过程 Technology,2005 数值模拟.北京科技大学学报,2000,22(5):417) (范悦宏.无网格法在数值传热学中的应用研究学位论文].南 [2]Dalrymple R A,Rogers B D.Numerical modeling of water waves 京:南京理工大学,2005) with the SPH method.Coastal Eng,2006,53(2-3):141 [13]Savage J,Pritchard W H.The problem of rupture of the billet in [3]Cingoski V,Miyamoto N,Yamashita H.Element-free Galerkin the continuous casting of steel.J Iron Steel Inst,1954,178(3):269 method for electromagnetic field computations.IEEE Trans Magn, [14]Li D H,Gao Y B,Xin Q B,et al.The processing method and 1998.34(5):3236 application study for latent heat releases in alloy castings. [4]Adams B,Wicke M.Meshless approximation methods and Foundry,2004,53(12):1005 applications in physics based modeling and animation (李东辉,高云宝,辛启斌,等.铸件凝固潜热的处理方法与应用 EUROGRAPHICS 2009.Munich,2009:213 研究.铸造,2004,53(12):1005) [5]Liu M B,Liu G R,Zong Z,et al.Computer simulation of high [15]Liu X.Meshless Method.Beijing:Science Press,2011 explosive explosion using smoothed particle hydrodynamics (刘欣.无网格方法.北京:科学出版社,2011) methodology.Compu Fluids,2003,32(3):305 [16]Belytschko T,Lu YY,Gu L.Element-free Galerkin methods.IntJ [6]Zhang L,Shen H F,Rong Y M,et al.Numerical simulation on Numer Methods Eng,1994,37(2):229 solidification and thermal stress of continuous casting billet in [17]Liu G R,Gu Y T.An Introduction to Meshfree Methods and Their mold based on meshless methods.Mater Sci Eng A,2007,466(1- Programming.Dordrecht:Springer,2005 2):71 [18]Wu S C.Liu G R.Cui X Y,et al.An edge-based smoothed point [7]Vertnik R,Sarler B.Solution of a continuous casting of steel interpolation method (ES-PIM)for heat transfer analysis of rapid benchmark test by a meshless method.Eng Anal Boundary Elem, manufacturing system.Int Heat Mass Transfer,2010,53(9-10): 2014,45:45 1938布置非均匀网格时网格过渡区域复杂的数据传 递,在非规则随机节点设置方面显示出极大的灵 活性. (3)相比于有限元基于网格的数值模拟方法, EFG 法回避了网格依赖性,具有良好的精度和自 适应性,为进一步探索坯壳重构、液/固界面追踪、 裂纹形成等网格模拟方法难以甚至无法处理的问 题,提供了高效、可行的数值计算方法. 参    考    文    献 Jing  D  J,  Cai  K  K.  Numerical  simulation  of  the  coupling phenomenon  between  thermal  and  mechanical  fields  of  billet  in continuous casting mold. J Univ Sci Technol Beijing, 2000, 22(5): 417 (荆德君, 蔡开科. 连铸结晶器内铸坯温度场和应力场耦合过程 数值模拟. 北京科技大学学报, 2000, 22(5):417 ) [1] Dalrymple R A, Rogers B D. Numerical modeling of water waves with the SPH method. Coastal Eng, 2006, 53(2-3): 141 [2] Cingoski  V,  Miyamoto  N,  Yamashita  H.  Element-free  Galerkin method for electromagnetic field computations. IEEE Trans Magn, 1998, 34(5): 3236 [3] Adams  B,  Wicke  M.  Meshless  approximation  methods  and applications  in  physics  based  modeling  and  animation  // EUROGRAPHICS 2009. Munich, 2009: 213 [4] Liu  M  B,  Liu  G  R,  Zong  Z,  et  al.  Computer  simulation  of  high explosive  explosion  using  smoothed  particle  hydrodynamics methodology. Comput Fluids, 2003, 32(3): 305 [5] Zhang  L,  Shen  H  F,  Rong  Y  M,  et  al.  Numerical  simulation  on solidification  and  thermal  stress  of  continuous  casting  billet  in mold based on meshless methods. Mater Sci Eng A, 2007, 466(1- 2): 71 [6] Vertnik  R,  Šarler  B.  Solution  of  a  continuous  casting  of  steel benchmark test by a meshless method. Eng Anal Boundary Elem, 2014, 45: 45 [7] Yamasaki N, Shima S, Tsunenari K, et al. Particle-based numerical analysis  of  spray  water  flow  in  secondary  cooling  of  continuous casting machines. ISIJ Int, 2015, 55(5): 976 [8] Vaghefi R, Hematiyan M R, Nayebi A. Three-dimensional thermo￾elastoplastic analysis of thick functionally graded plates using the meshless  local  Petrov  -  Galerkin  method. Eng Anal Boundary Elem, 2016, 71: 34 [9] Hostos  J  C  Á,  Bencomo  A  D,  Cabrera  E  S  P.  Simple  iterative procedure  for  the  thermal-mechanical  analysis  of  continuous casting processes using the element-free Galerkin method. J Therm Stresses, 2018, 41(2): 160 [10] Hu P H, Wang X D, Wei J J, et al. Investigation of liquid/solid slag and  air  gap  behavior  inside  the  mold  during  continuous  slab casting. ISIJ Int, 2018, 58(5): 892 [11] Fan  Y  H. A Study of Meshless Method in Numerical Heat Transfer[Dissertation]. Nanjing: Nanjing University of Science & Technology, 2005 (范悦宏. 无网格法在数值传热学中的应用研究[学位论文]. 南 京: 南京理工大学, 2005) [12] Savage J, Pritchard W H. The problem of rupture of the billet in the continuous casting of steel. J Iron Steel Inst, 1954, 178(3): 269 [13] Li  D  H,  Gao  Y  B,  Xin  Q  B,  et  al.  The  processing  method  and application  study  for  latent  heat  releases  in  alloy  castings. Foundry, 2004, 53(12): 1005 (李东辉, 高云宝, 辛启斌, 等. 铸件凝固潜热的处理方法与应用 研究. 铸造, 2004, 53(12):1005 ) [14] Liu X. Meshless Method. Beijing: Science Press, 2011 (刘欣. 无网格方法. 北京: 科学出版社, 2011) [15] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. Int J Numer Methods Eng, 1994, 37(2): 229 [16] Liu G R, Gu Y T. An Introduction to Meshfree Methods and Their Programming. Dordrecht: Springer, 2005 [17] Wu S C, Liu G R, Cui X Y, et al. An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system. Int J Heat Mass Transfer, 2010, 53(9-10): 1938 [18] 王    宁等: 基于无网格伽辽金法的连铸坯凝固计算方法 · 193 ·
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