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ORIGINAL RESEARCH

Semianalytical Solution for Two-Phase Flow in Porous Media with a Discontinuity

Radek Fuík^a, Jirí Mikyka^a, Michal Bene^a,* and Tissa H. Illangasekare^b

^a Dep. of Mathematics, Faculty of Nuclear Science and Physical Engineering, Czech Technical Univ., Trojanova 13, 120 00 Prague, Czech Republic
^b Center for Experimental Study of Subsurface Environmental Processes (CESEP), Div. of Environmental Science and Engineering, Colorado School of Mines, 1500 Illinois St., Golden CO 80401
^* Corresponding author (benes{at}km1.fjfi.cvut.cz).

Received 13 September 2007.

We present a benchmark solution for one-dimensional porous media with heterogeneity involving two soils separated by a sharp interface. A similar problem was discussed previously by other researchers; however, only a diffusion term was considered in their models. The proposed solution allows the inclusion of advection terms in a limited way. This solution is useful in the verification of more complex numerical models of multiphase flow developed for general applications involving heterogeneous aquifers. A derivation of the semianalytical solution for heterogeneous porous media is presented and its existence and uniqueness are discussed. A computationally efficient algorithm and several computational results are presented.