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The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

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Abstract

For compressible two-phase displacement problem, the modified upwind finite difference fractional steps schemes are put forward. Some techniques, such as calculus of variations, commutative law of multiplication of difference operators, decomposition of high order difference operators, the theory of prior estimates and techniques are used. Optimal order estimates in L 2 norm are derived for the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.

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References

  1. 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 equations. J. Inst. Maths. Applics., 23: 321–337 (1979)

    Article  MATH  Google Scholar 

  2. Douglas, J.Jr. Finite difference methods for two-phase incompressible flow in porous media. SIAM J. Numer. Anal., 20(4): 681–696 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  3. Douglas, J.Jr., Roberts, J.E. Numerical method for a model for compressible miscible displacement in porous media. Math. Comp., 4(164): 441–459 (1983)

    Article  Google Scholar 

  4. 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. SIAM J. Numer. Anal., 19(5): 781–895 (1982)

    Article  MathSciNet  Google Scholar 

  5. Douglas, J.Jr. Simulaton of miscible displacement in porous media by a modified method of characteristic procedure, Lecture Notes in Mathematics 912, Numerical Analysis, Proceedings, Dundee, 1981

  6. Ewing, R.E. The Mathematics of Reservoir Simulation. SIAM; Philadelphia, 1983

  7. Ewing, R.E., Lazarov, R.D., Vassilevski, P.S. Finite difference shceme for parabolic problems on composite grids with refinement in time and space. SIAM J. Numer. Anal., 31(6): 1605–1622 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  8. 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. Comp. Meth. Appl. Mech. Eng., 47(1–2): 73–92 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lazarov, R.D., Mishev, I.D., Vassilevski, P.S. Finite volume method for convection-diffusion problems. 33(1): 31–55 (1996)

  10. Marchuk, G.I. Splitting and alternating direction method. In: Ciarlet, P.G., Lions, J.L., eds. Handbook of Numerical Analysis. Elsevior Science Publishers BV, Paris, 197–460 1990

  11. Yuan, Yi-rang. Characteristic finite difference methods for moving boundary value problem of numerical simulation of oil deposit. Science of China, 37(A) (12): 1442–1453 (1994)

    MATH  Google Scholar 

  12. Yuan, Yi-rang. The characteristic mixed-finite element method and analysis for three-dimensional moving boundary value problem. Science in China, 39(A) (3): 276–288 (1996)

    MATH  Google Scholar 

  13. Yuan, Yi-rang. Finite difference method and analysis for three-dimensional simiconductor device of heat conduction. Science in China, 39(A)(11): 1140–1151 (1996)

    MATH  Google Scholar 

  14. Yuan, Yi-rang. Finite difference methods for a compressible miscible displacement problem in porous media. Math. Numer. Sinica, 15(1): 16–28 (1993)

    MATH  MathSciNet  Google Scholar 

  15. Yuan, Yi-rang. Time stepping along characteristics for the finite element approximation of compressible miscible displacement in porous media. Math. Numer. Sinica, 14(4): 385–406 (1992)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, China

    Yi-rang Yuan

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  1. Yi-rang Yuan
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Correspondence to Yi-rang Yuan.

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Supported by the Major State Basic Research Program of China (Grant No. 1999032803), the National NaturalScience Foundation of China (Grant No.10372052, 10271066) and the Decorate Foundation of the Ministry Education of China (Grant No. 20030422047)

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Yuan, Yr. The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem. Acta Mathematicae Applicatae Sinica, English Series 20, 381–396 (2004). https://doi.org/10.1007/s10255-004-0177-8

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  • DOI: https://doi.org/10.1007/s10255-004-0177-8

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