A New Class of Entropy Solutions of the Buckley-Leverett Equation

@article{Duijn2007ANC,
  title={A New Class of Entropy Solutions of the Buckley-Leverett Equation},
  author={C. J. van Duijn and L. A. Peletier and Iuliu Sorin Pop},
  journal={SIAM J. Math. Analysis},
  year={2007},
  volume={39},
  pages={507-536}
}
We discuss an extension of the Buckley–Leverett (BL) equation describing two-phase flow in porous media. This extension includes a third order mixed derivatives term and models the dynamic effects in the pressure difference between the two phases. We derive existence conditions for traveling wave solutions of the extended model. This leads to admissible shocks for the original BL equation, which violate the Oleinik entropy condition and are therefore called nonclassical. In this way we obtain… CONTINUE READING

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References

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SHOWING 1-10 OF 30 REFERENCES

Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries

  • S. M. Hassanizadeh, W. G. Gray
  • Adv. Water Resour., 13
  • 1990
Highly Influential
6 Excerpts

Experimental measurements of saturation overshoot on infiltration

  • D. A. DiCarlo
  • Water Resour. Res., 40
  • 2004
1 Excerpt

A model problem for groundwater flow with dynamic capillary pressure: Stability of travelling waves

  • C. Cuesta, J. Hulshof
  • Nonlinear Anal., 52
  • 2003
1 Excerpt

Pseudo-Parabolic Equations with Driving Convection Term

  • C. Cuesta
  • Ph.D. thesis, VU Amsterdam, The Netherlands
  • 2003

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