Characteristic Finite Difference Method and Application for Moving Boundary Value Problem of the Coupled System
-
摘要: 油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对合理评估油气资源的勘探和开发有重要的价值.其数学模型是一组多层对流扩散耦合系统的动边值问题.提出一类特征差分格式,得到最佳阶误差估计结果.对这一领域的模型分析、数值方法和软件研制均有重要的理论和实用价值.Abstract: The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes was put forward,from which optimal order estimates in norm was derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,for model numerical method and for software development.
-
[1] Ewing R E.The Mathematics of Reservoir Simulation[M].Philadelphia:SIAM, 1983. [2] Bredehoeft J D, Pinder G F. Digital analysis of area flow in multiaquifer ground water systems: A quasi-three-dimensional model[J].Water Resources Research,1970,6(3):883-888. doi: 10.1029/WR006i003p00883 [3] Don W, Emil O F. An iterative quasi-three-dimensional finite element model for heterogeneous multiaquifer systems[J].Water Resources Research,1978,14(5):943-952. doi: 10.1029/WR014i005p00943 [4] Ungerer P, Dolyiez B, Chenet P Y,et al.A 2-D model of basin petroleum by two-phase fluid flows,application to some case studies[A].In:Doligez B,Ed.Migration of Hydrocarbon in Sedimentary Basins[C].Paris: Editions Techniq, 1987, 414-455. [5] Ungerer P. Fluid flow, hydrocarbon generation and migration[J].AAPG Bull, 1990,74(3):309-335. [6] Douglas Jr J, Russell T F. Numerical method for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures[J].SIAM J Numer Anal,1982,19(5):871-885. doi: 10.1137/0719063 [7] Douglas Jr J. 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 [8] 袁益让. 可压缩两相驱动问题的分数步长特征差分格式[J]. 中国科学,A辑,1998,28(10):893-902. [9] 萨马尔斯基A A,安德烈耶夫B B. 椭圆型方程差分方法[M]. 武汉大学计算数学教研室 译.北京:科学出版,1984. [10] 袁益让. 多层渗流方程组合系统的迎风分数步长差分方法和应用[J]. 中国科学,A辑,2001,31(9):791-806. [11] 袁益让. 三维非线性多层渗流方程耦合系统的差分方法[J]. 中国科学,A辑,2005,35(12):1397-1423.
计量
- 文章访问数: 2969
- HTML全文浏览量: 144
- PDF下载量: 588
- 被引次数: 0