Geodesic
Mixed variable technique for simulating unsaturated-saturated flows
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 4, pp. 58-72

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Mixed variable technique for simulating unsaturated-saturated flows is proposed. It based on a new form of governing equation in term of mixed variable and finite elements method with numerical integration. For homogeneous medium new variable coincides with saturation in one regions and with “normalized” pressure head otherwise. Efficient algorithm for solving discrete problem is proposed. Сomputational accuracy and robustness of the method are demonstrated by solving four test problems. 
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     author = {A. A. Akhtareev and R. Z. Dautov},
     title = {Mixed variable technique for simulating unsaturated-saturated flows},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {58--72},
     publisher = {mathdoc},
     volume = {149},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2007_149_4_a4/}
}
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A. A. Akhtareev; R. Z. Dautov. Mixed variable technique for simulating unsaturated-saturated flows. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 4, pp. 58-72. http://geodesic.mathdoc.fr/item/UZKU_2007_149_4_a4/