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An Overview of the Modified Buckley–Leverett Equation

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Integral Methods in Science and Engineering

Abstract

We study the modified Buckley-Leverett (BL) equation, which is a simple model for two-phase fluid in a porous medium.

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References

  1. Bona, J. L. and Luo, L.-H.: Initial-boundary value problems for model equations for the propagation of long waves. Lecture Notes in Pure and Appl. Math., 168, 63, 65–94 (1995)

    MathSciNet  Google Scholar 

  2. Bona, J.L., Chen, H.-Q., Sun, S.M., and Zhang, B.-Y.: Comparison of quarter-plane and two-point boundary value problems: the BBM-equation. Discrete Contin. Dyn. Syst., 13(4), 921–940 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Buckley, S.E. and Leverett, M.C.: Mechanism of fluid displacement in sands. Petroleum Transactions, AIME, 146, 107–116 (1942)

    Article  Google Scholar 

  4. Cockburn, B., Johnson, C., Shu, C.-W., and Tadmor, E.: Advanced numerical approximation of nonlinear hyperbolic equations. Lecture Notes in Mathematics, Papers from the C.I.M.E. Summer School held in Cetraro, June 23–28, 1997, 1697 (1998)

    Google Scholar 

  5. Cockburn, B., Karniadakis, G. E., and Shu, C.-W. (Eds.): Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Computational Science and Engineering (2000)

    Google Scholar 

  6. DiCarlo, D. A.: Experimental measurements of saturation overshoot on infiltration. Water Resources Research, 40, 4215.1 – 4215.9 (2004)

    Article  Google Scholar 

  7. Hassanizadeh, S.M. and Gray, W.G.: Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour., 13, 169–186 (1990)

    Article  Google Scholar 

  8. Hassanizadeh, S.M. and Gray, W.G.: Thermodynamic basis of capillary pressure in porous media. Water Resour. Res., 29, 3389–3405 (1993)

    Article  Google Scholar 

  9. Kurganov, A. and Levy, D.: A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput., 22(4), 1461–1488 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. LeVeque, R.J.: Numerical methods for conservation laws. Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel (1992)

    Book  MATH  Google Scholar 

  11. LeVeque, R.J.: Finite volume methods for hyperbolic problems. Cambridge University Press, 2002

    Google Scholar 

  12. Liu, X.-D. and Tadmor, E.: Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math., 79(3), 397–425 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Nessyahu, H. and Tadmor, E.: Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys., 87(2), 408–463 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Van Duijn, C.J., Mikelic, A., and Pop, I.S.: Effective Buckley-Leverett equations by homogenization. Progress in industrial mathematics at ECMI, 42–52 (2000).

    Google Scholar 

  15. Van Duijn, C.J., Mikelic, A., and Pop, I.S.: Effective Equations for Two-Phase Flow with Trapping on the Micro Scale. SIAM Journal on Applied Mathematics, 62(5), 1531–1568 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Van Duijn, C.J., Peletier, L.A., and Pop, I.S.: A new class of entropy solutions of the Buckley-Leverett equation. SIAM J. Math. Anal., 39(2), 507–536 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wang, Y.: Central schemes for the modified Buckley-Leverett equation. Ph.D. thesis, The Ohio State University (2010).

    Google Scholar 

  18. Wang, Y. and Kao, C.-Y.: Central schemes for the modified Buckley-Leverett equation. Journal of Computational Science, 4(1), 12–23 (2013)

    Article  Google Scholar 

  19. Wang, Y. and Kao, C.-Y.: Bounded Domain Problem for the Modified Buckley-Leverett Equation. Journal of Dynamics and Differential Equations, 26(3),607–629 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  20. Xu, Y. and Shu, C-W.: A local discontinuous Galerkin method for the Camassa-Holm equation. SIAM J. Numer. Anal., 46(4), 1998–2021 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Xu, Y. and Shu, C-W.: Local discontinuous Galerkin method for the Hunter-Saxton equation and its zero-viscosity and zero-dispersion limits. SIAM J. Sci. Comput., 31(2), 1249–1268 (2008/09)

    Google Scholar 

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Acknowledgements

This research was supported in part by a Faculty Investment Program and a Junior Faculty Fellow Program grant from the Research Council and College of Arts and Sciences of the University of Oklahoma Norman Campus.

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Authors and Affiliations

  1. University of Oklahoma, 601 Elm Avenue, Norman, OK, 73019, USA

    Y. Wang

Authors
  1. Y. Wang
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Correspondence to Y. Wang .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tulsa, Department of Mathematics, Oklahoma, Oklahoma, USA

    Christian Constanda

  2. Department of Mathematics, Karlsruhe Institute of Technology, Department of Mathematics, Karlsruhe, Germany

    Andreas Kirsch

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Wang, Y. (2015). An Overview of the Modified Buckley–Leverett Equation. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_55

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