YUAN Yi-rang, LIANG Dong, RUI Hong-xing, DU Ning, WANG Wen-qia. Numerical Method for the Nonlinear Two-Phase Displacement Problem and Its Application[J]. Applied Mathematics and Mechanics, 2008, 29(5): 575-588.
Citation: YUAN Yi-rang, LIANG Dong, RUI Hong-xing, DU Ning, WANG Wen-qia. Numerical Method for the Nonlinear Two-Phase Displacement Problem and Its Application[J]. Applied Mathematics and Mechanics, 2008, 29(5): 575-588.

Numerical Method for the Nonlinear Two-Phase Displacement Problem and Its Application

  • Received Date: 2007-09-20
  • Rev Recd Date: 2008-03-24
  • Publish Date: 2008-05-15
  • For the three-dimensional nonlinear two-phase displacement problem,the modified up-wind finite difference fractional steps schemes were put forward'some techniques,such as calculus of variations,induction hypothesis,decomposition of high order difference operators,the theory of prior estimates and techniques were used.Optimal order estimates were derived for the error in the approximation solution.These methods have been successfully used in predicting the consequences of seawater intrusion and protection projects.
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  • [1]
    袁益让,梁栋,芮洪兴.海水入侵防治工程的后效预测数学模型[A].见:姜福德 主编.山东省第二届数学研讨会论文集[C].青岛:青岛海洋大学出版社,1995,1-5.
    [2]
    袁益让,梁栋,芮洪兴.海水入侵及防治工程的预测模拟[A].见: 赵德山 主编.海水入侵灾害防治研究[C].济南: 山东科技出版社,1996,198-204.
    [3]
    雅·贝尔.地下水水力学[M].许涓铭 译.北京: 地质出版社,1985.
    [4]
    Douglas Jr J,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 Numer Anal,1982,19(5):881-895.
    [5]
    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
    [6]
    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].Comput Methods Appl Mech Engrg,1984,47(1/2):73-92. doi: 10.1016/0045-7825(84)90048-3
    [7]
    Douglas Jr J,Roberts J E.Numerical method for a model for compressible miscible displacement in porous media[J].Math Comp,1983,4(164):441-459.
    [8]
    Ewing R E.The Mathematics of Reservoir Simulation[M].Philadelphia: SIAM,1983.
    [9]
    Douglas Jr J,YUAN Yi-rang.Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with mixed finite element procedure[A].In: Wheeler,Ed.Numerical Simulation in Oil Recovery[C].Minnesota: Springer-Verlag,1986,119-131.
    [10]
    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
    [11]
    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
    [12]
    Peaceman D W.Fundamentals of Numerical Reservoir Simulation[M].Amsterdam: Elsevier,1980.
    [13]
    N·N·雅宁柯.分数步法[M].周宝熙,林鹏 译.北京:科学出版社,1992.
    [14]
    Douglas Jr J,Gunn J E.Two order correct difference analogues for the equation of multidimensional heat flow[J].Math Comp,1963,17(81):71-80. doi: 10.1090/S0025-5718-1963-0149676-2
    [15]
    Douglas Jr J,Gunn J E.A general formulation of alternation methods—part 1:parabolic and hyperbolic problems[J].Numer Math,1964,9(5):428-453.
    [16]
    Ewing R E.Mathematical modeling and simulation for multiphase flow in porous media[A].In:CHEN Zhang-xin,Ewing R E,Shi Z C,Eds.Numerical Treatment of Multiphase Flows in Porous Media[C].Lecture Notes in Physics.V 552.New York: Springer,2000,19-29.
    [17]
    薛禹群,谢春红,胡吉春,等.海水入侵咸淡水界面运移规律研究[M].南京: 南京大学出版社,1991.
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