Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values
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摘要: 可压缩可混溶油、水渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值,其数学模型是一组非线性耦合偏微分方程组的动边值问题.对二维有界域的动边值问题提出一类新的迎风差分格式,应用区域变换、变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到了最佳误差估计结果.该方法已成功应用到油资评估的数值模拟中.它对这一领域的模型分析,数值方法和软件研制均有重要的价值.Abstract: The research of the miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwindfinite difference schemes were put forward. Some techniques, such as calculus of variations, change of variables, theory of a priori estimates and techniques were adopted. Optmial orderestmiates are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development.
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[1] 袁益让.油藏数值模拟中动边值问题的特征差分方法[J].中国科学,A辑,1994,24(10):1029-1036. [2] Douglas J Jr,Roberts J E.Numerical method for a model for compressible miscible displacement in porous media[J].Math Comp,1983,41(164):441-459. doi: 10.1090/S0025-5718-1983-0717695-3 [3] 袁益让.多孔介质中可压缩、可混溶驱动问题的特征有限元方法[J].计算数学,1992,14(4):385-406. [4] 袁益让.在多孔介质中完全可压缩、可混溶驱动问题的差分方法[J].计算数学,1993,15(1):16-28. [5] Ewing R E.The Mathematics of Reservoir Simulation[M].Philadelphia:SIAM,1983. [6] Marchuk G I.Splitting and alternating direction method[A].In:Ciarlet P G,Lions J L,Eds.Handbook of Numerical Analysis[C].Paris:Elsevior Science Publishers B V,1990,197-460. [7] Douglas J Jr,Russell T F.Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures[J].SIAM J Nume Anal,1982,19(5):781-895. doi: 10.1137/0719054 [8] Douglas J Jr.Simulation of miscible displacement in porous media by a modified method of characteristic procedure[A]. In:Lecture Notes in Mathematics 912,Numerical Analysis[C].Berlin:Springer,1982,64-70. [9] Douglas J Jr.Finite difference methods for two-phase incompressible flow in porous media[J].SIAM J Numer Anal,1983,20(4):681-696. doi: 10.1137/0720046 [10] Ewing R E,Russell T F,Wheeler M F.Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics[J].Comp Meth Appl Mech Eng,1984,47(1/2):73-92. doi: 10.1016/0045-7825(84)90048-3 [11] Ewing R E,Russell T F,Wheeler M F.Simulation of miscible displacement using mixed methods and a modified method of characteristics[A].In:SPE 12241,7th SPE Symposium on Reservoir Simulation[C].San Francisco,1983. [12] 袁益让.三维动边值问题的特征混合元方法和分析[J].中国科学,A 辑,1996,26(1):11-22. [13] 袁益让.三维热传导型半导体问题的差分方法和分析[J].中国科学,A 辑,1996,26(11):973-983. [14] Axelsson O,Gustafasson I.A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of equation[J].J Inst Maths Applics,1979,23(3):321-337. doi: 10.1093/imamat/23.3.321 [15] Ewing R E,Lazarov R D,Vassilevski A T.Finite difference scheme for parabolic problems on composite grids with refinement in time and space[J].SIAM J Numer Anal,1994,31(6):1605-1622. doi: 10.1137/0731083 [16] Lazarov R D,Mishev I D,Vassilevski P S.Finite volume method for convection-diffusion problems[J].SIAM J Numer Anal,1996,33(1):31-55. doi: 10.1137/0733003 [17] Peaceman D W.Fundamental of Numerical Reservoir Simulation[M].Amsterdam:Elsevier,1980. [18] Ewing R E.Mathematical modeling and simulation for multiphase flow in porous media[A].In:Numerical Treatment of Multiphase Flows in Porous Media[C].Lecture Notes in Physics,Vol 1552,New York:Springer,2000,43-57. [19] YUAN Yi-rang,HAN Yu-ji.Numerical simulation of migration-accumulation of oil resources[J].Comput Geosi,2008,12:153-162. doi: 10.1007/s10596-007-9075-5 [20] 袁益让,韩玉笈.三维油资源渗流力学运移聚集的大规模数值模拟和应用[J].中国科学,G辑,2008,38(11):1582-1600. [21] 袁益让,羊丹平,王文洽.含油气盆地三维问题的计算机模拟及其数值分析[J].计算物理,1992,9(4):361-365.
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