适应于界面大变形的高分辨率中心型ALE方法
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摘要
针对基于积分形式的Euler方程组耦合质量组份模型方程而发展的多介质整体ALE方法耗散大的问题,采用基于微分形式的Euler方程组所发展的高分辨率界面反耗散的思想来控制界面处的数值耗散,发展了一种二维平面中积分意义下的耦合质量组份方程和体积组份方程的界面反耗散的高分辨率多介质中心型ALE方法,从而高分辨率地模拟大变形物质界面.
For the large dissipation problem of the multimaterial Global ALE method based on the Euler equation with integral form combined with the mass fraction equation, we use the high resolution anti-difusive idea for interface based on the Euler equation with diferential form to control the numerical difusion at interface, and then we developed a multimaterial cell-centered ALE method based on the Euler equation with integral form combined with the mass fraction equation and volume fraction equation in plane coordinate to simulate the large deformation multimaterial interface with high resolution.
For the large dissipation problem of the multimaterial Global ALE method based on the Euler equation with integral form combined with the mass fraction equation, we use the high resolution anti-difusive idea for interface based on the Euler equation with diferential form to control the numerical difusion at interface, and then we developed a multimaterial cell-centered ALE method based on the Euler equation with integral form combined with the mass fraction equation and volume fraction equation in plane coordinate to simulate the large deformation multimaterial interface with high resolution.
引文
1 Benson J.Computational methods in Lagrangian and Eulerian hydrocodes.Comput Methods Appl Mech Eng,1992,99:235
2 Addession FL,Baumgardner JR,Dukowicz JK.CAVEAT:A computer code for fluid dynamics problem with large distortion and internal slip,Los Alamos report LA-10613-MS,1992
3 田保林,申卫东,刘妍等.ALE框架下几种不同Godunov型格式的数值比较研究,计算物理,2007,24(5):537-542(Tian Baolin,Shen Weidong,Liu Yan,et al.Numerical study on several Godunovtype shemes with ALE formulation.Computational Physics,2007,24 (5):537-542(in Chinese))
4 Knupp P,Margolin G,Shashkov M.Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods.J Comput Phys,2002,176:193
5 Glimm J,Li XL,Liu YJ,et al.Conservativ front-tracking with improved accuracy.SIAM J Numer Anal,2003,41(5):1926-1947
6 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.J Comp Physics,1981,39:201-225
7 Barlow A.A compatible finite elements multi-material ALE hydrodynamics algorithm.Int J Numer Mentods for Fluids,2008,56(8):953-964
8 Multimat.International Conference/Workshop on Numerical Methods for Multi-material Fluid Flows,http://www.icfd.reading.ac.uk/Multimaterial-Workshop.htm,(2005),http://kfe.fjfi.cut.cz/~multimat2007,(2007),http://www.eucentre.it/multimat09,(2009)
9 Fedkiw RP,Aslam T,Merriman B,et al.A non-oscillatory Eulerian approach to interfaces in multimaterial flows(the Ghost Fluid Method).J Comput Phys,1999,152:457-492.
10 Abgrall R,Karni S.Computations of compressible multifluids.J Comput Phys,2001,169:594
11 田保林,刘妍,申卫东等.可压缩多介质流动的整体ALE方法.北京理工大学学报,2010,30(5):622-625(Tian Baolin,Liu Yan,Shen Weidong,et al.A global arbitrary Lagrangian--Eulerian method for compressible multimaterial fluid flows.Journal of Beijing Institute of Technology,2010,30(5):622-625(in Chinese))
12 Despres B,Lagoutiere F.Numerical resolution of a two-component compressible fluid model with interface.Prog Comp Fluid Dyn,2007,7(6):295-310
13 Kokh S,Lagoutiere F.An anti-difusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model.J Comput Phys,2010,229:2773-2809
14 Allaire G,Clerc S,Kokh S,A five-equation model for the simulation of interfaces between compressible fluid.J Comput Phys,2002,181(2):577-616
15 Toro EF.Riemann Solvers and Numerical Methods for Fluid Dynamics.Berlin,Heidelberg:Springer-Verlag,2009
16 Brackbill JU,Saltzman JS.Adaptive zoning for singular problem in two dimension.J Comput Phys,1982,46:342-368
17 Murrone A,Guillard H.A five equation reduced model for compressible two phase flow problem.J Comput Phys,2005,202:664-698
18 Galera S,Maire PH,Breil J.A two-dimensional unstructured cellcentered multi-material ALE scheme using VOF interface reconstruction.J Comput Phys,2010,229:5755-5787
2 Addession FL,Baumgardner JR,Dukowicz JK.CAVEAT:A computer code for fluid dynamics problem with large distortion and internal slip,Los Alamos report LA-10613-MS,1992
3 田保林,申卫东,刘妍等.ALE框架下几种不同Godunov型格式的数值比较研究,计算物理,2007,24(5):537-542(Tian Baolin,Shen Weidong,Liu Yan,et al.Numerical study on several Godunovtype shemes with ALE formulation.Computational Physics,2007,24 (5):537-542(in Chinese))
4 Knupp P,Margolin G,Shashkov M.Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods.J Comput Phys,2002,176:193
5 Glimm J,Li XL,Liu YJ,et al.Conservativ front-tracking with improved accuracy.SIAM J Numer Anal,2003,41(5):1926-1947
6 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.J Comp Physics,1981,39:201-225
7 Barlow A.A compatible finite elements multi-material ALE hydrodynamics algorithm.Int J Numer Mentods for Fluids,2008,56(8):953-964
8 Multimat.International Conference/Workshop on Numerical Methods for Multi-material Fluid Flows,http://www.icfd.reading.ac.uk/Multimaterial-Workshop.htm,(2005),http://kfe.fjfi.cut.cz/~multimat2007,(2007),http://www.eucentre.it/multimat09,(2009)
9 Fedkiw RP,Aslam T,Merriman B,et al.A non-oscillatory Eulerian approach to interfaces in multimaterial flows(the Ghost Fluid Method).J Comput Phys,1999,152:457-492.
10 Abgrall R,Karni S.Computations of compressible multifluids.J Comput Phys,2001,169:594
11 田保林,刘妍,申卫东等.可压缩多介质流动的整体ALE方法.北京理工大学学报,2010,30(5):622-625(Tian Baolin,Liu Yan,Shen Weidong,et al.A global arbitrary Lagrangian--Eulerian method for compressible multimaterial fluid flows.Journal of Beijing Institute of Technology,2010,30(5):622-625(in Chinese))
12 Despres B,Lagoutiere F.Numerical resolution of a two-component compressible fluid model with interface.Prog Comp Fluid Dyn,2007,7(6):295-310
13 Kokh S,Lagoutiere F.An anti-difusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model.J Comput Phys,2010,229:2773-2809
14 Allaire G,Clerc S,Kokh S,A five-equation model for the simulation of interfaces between compressible fluid.J Comput Phys,2002,181(2):577-616
15 Toro EF.Riemann Solvers and Numerical Methods for Fluid Dynamics.Berlin,Heidelberg:Springer-Verlag,2009
16 Brackbill JU,Saltzman JS.Adaptive zoning for singular problem in two dimension.J Comput Phys,1982,46:342-368
17 Murrone A,Guillard H.A five equation reduced model for compressible two phase flow problem.J Comput Phys,2005,202:664-698
18 Galera S,Maire PH,Breil J.A two-dimensional unstructured cellcentered multi-material ALE scheme using VOF interface reconstruction.J Comput Phys,2010,229:5755-5787