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Central Schemes for the Modified Buckley-Leverett Equation
Wang, Ying

2010, Doctor of Philosophy, Ohio State University, Mathematics.

In fluid dynamics, the Buckley-Leverett (BL) equation is a transport equation used to model two-phase flow in porous media. One application is secondary recovery by water-drive in oil reservoir simulation. The modified Buckley-Leverett (MBL) equation differs from the classical BL equation by including a balanced diffusive-dispersive combination. The dispersive term is a third order mixed derivatives term, which models the dynamic effects in the pressure difference between the two phases. The classical BL equation gives a monotone water saturation profile for any Riemann problem; on the contrast, when the dispersive parameter is large enough, the MBL equation delivers non-monotone water saturation profile for certain Riemann problems as suggested by the experimental observations.


In this thesis, we first show that the solution of the finite interval [0,L] boundary value problem converges to that of the half-line [0,+∞) problem for the MBL equation as L → +∞. This result provides a justification for the use of the finite interval boundary value problem in numerical studies for the half line problem.


Furthermore, we extend the classical central schemes for the hyperbolic conservation laws to solve the MBL equation which is of pseudo-parabolic type.
This extension can also be applied to other conservation law solvers. Numerical results confirm the existence of non-monotone water saturation profiles consisting of constant states separated by shocks, which is consistent to the experimental observations.


The two-dimensional physical space is a general setting for the underground oil recovery. In this thesis, we also include the derivation of the two-dimensional extension of the MBL equation.

Chiu-Yen Kao (Advisor)
Avner Friedman (Committee Member)
Fei-Ran Tian (Committee Member)

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Wang, Y. (2010). Central Schemes for the Modified Buckley-Leverett Equation. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Wang, Ying. "Central Schemes for the Modified Buckley-Leverett Equation." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Wang, Ying "Central Schemes for the Modified Buckley-Leverett Equation." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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