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R. E. Ewing and H. Wang, “A Summary of Numerical Methods for Time-Dependent Advection Dominated Partial Differential Equations,” Journal of Computational and Applied Mathematics, Vol. 128, No. 1-2, 2001, pp. 423-445. doi:10.1016/S0377-0427(00)00522-7

has been cited by the following article:

• TITLE: Pressure/Saturation System for Immiscible Two-Phase Flow: Uniqueness Revisited

  AUTHORS: Koffi B. Fadimba

  KEYWORDS: Porous Medium, Uniqueness of a Solution, Degenerate Equation, Immiscible Two-Phase Flow, Regularization, Phase Mobility.

  JOURNAL NAME: Applied Mathematics, Vol.2 No.5, May 6, 2011

  ABSTRACT: We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct mobilities (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed mobilities, we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.