Geodesic
Regularization of a discrete scheme for a three-dimensional problem of the evolution of the interface of different fluids
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 557-562 
D. N. Nikol'skiǐ. Regularization of a discrete scheme for a three-dimensional problem of the evolution of the interface of different fluids. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 557-562. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A regularized discrete scheme is developed that describes the three-dimensional evolution of the interface between fluids with different viscosities and densities in the Leibenzon–Muskat model. The regularization is achieved by smoothing the kernel of the singular integral involved in the differential equation governing the moving interface. The discrete scheme is tested by solving the problem of a drop of one fluid evolving in a translational flow of another.

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