Geodesic
Solving the Buckley--Leverett equation with a random coefficient of porosity
Numerical methods and programming, Tome 13 (2012) no. 4, pp. 517-524.

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The Buckley–Leverett equation with a random coefficient of porosity is considered. In order to analyze the equation, a combination of analytical (the method of characteristics) and numerical (upwind and hybrid difference schemes) approaches is used. An explicit expression for the stochastic characteristics of the Buckley–Leverett equation is obtained. The statistical parameters of breakthrough time are considered. A comparison between the analytical estimates and the numerical results is discussed.
Keywords: Buckley–Leverett equation; geostatistics; hybrid difference schemes. 
@article{VMP_2012_13_4_a4,
     author = {A. V. Isaeva and M. L. Serdobol'skaya},
     title = {Solving the {Buckley--Leverett} equation with a random coefficient of porosity},
     journal = {Numerical methods and programming},
     pages = {517--524},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_4_a4/}
}
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A. V. Isaeva; M. L. Serdobol'skaya. Solving the Buckley--Leverett equation with a random coefficient of porosity. Numerical methods and programming, Tome 13 (2012) no. 4, pp. 517-524. http://geodesic.mathdoc.fr/item/VMP_2012_13_4_a4/