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多孔介质中三维混溶驱动问题在三角剖分复合网格上的有限差分格式

刘伟(1),袁益让(2)   

  1. (1)山东经济学院统计与数学学院, 济南 250014;(2)山东大学数学研究所, 济南 250100
  • 收稿日期:2007-06-05 修回日期:2009-12-16 出版日期:2010-07-25 发布日期:2010-07-25

刘伟;袁益让. 多孔介质中三维混溶驱动问题在三角剖分复合网格上的有限差分格式[J]. 系统科学与数学, 2010, 30(7): 963-978.

LIU Wei ;YUAN Yirang. Finite Difference Schemes for Three-Dimensional Miscible Displacement Flow in Porous Media on Triangular Composite Grids[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(7): 963-978.

Finite Difference Schemes for Three-Dimensional Miscible Displacement Flow in Porous Media on Triangular Composite Grids

LIU Wei (1), YUAN Yirang(2)   

  1. (1)School of Statistics and Mathematics, Shandong Economic University, Jinan 250014;(2)School of Mathematics and System Science, Shandong University, Jinan 250100
  • Received:2007-06-05 Revised:2009-12-16 Online:2010-07-25 Published:2010-07-25
针对多孔介质中不可压缩流体的混溶驱动问题,基于平衡方程,利用有限体积方法建立了其三维问题在三角剖分单元中心空间局部加密复合网格上的有限差分格式,分析了差分格式的稳定性和收敛性,得到了关于饱和度的能量模误差估计,最后给出了数值算例.
Based on the balance equation, finite difference schemes for three-dimensional miscible displacement flow in porous media on triangular cell-centered grids with local refinement in space are constructed. Their stability and convergence are given, the error estimate in the energy norm is obtained. Finally, a numerical example is given.

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[1] 李远清. 一类常微分方程组周期解构造的耦合方法[J]. 系统科学与数学, 1998, 18(2): 167-176.
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