Group classifi cation of diff erence schemes of parabolic diff erential equations of one- and two-phase fl ow in porous media

Markov Pavel

The purpose of this study is to find classes of difference schemes with continuous symmetry groups and practical applications in the field of modeling of filtration processes in porous media. The classes of difference schemes with continuous symmetry groups are found in this article based on the well-known method of difference schemes construction with the preservation of continuous symmetry groups of original differential equations. Group classifications of difference schemes for differential equations of gas flow and two-phase flow within the Rapoport-Leas problem are obtained on the basis of known group classifications of corresponding parabolic differential equations and the mentioned method. A generalization for multidimensional cases is obtained for the found classes of difference schemes. The obtained classes can be used to accelerate numerical calculations when modeling mentioned in the article types of processes of one- and two-phase flow on micro- and macroscales of porous media.

Keywords:continuous symmetry group; group classification of difference schemes; one-phase gas flow; parabolic differential equations; porous media; Rapoport-Leas equation; two-phase flow of water and oil.