Hierarchy of explicit-implicit difference schemes for multiphase filtration problems

The paper is devoted to construction and investigation of explicit-implicit schemes for multiphase multicomponent filtration. The propose of this paper is to consider cell values as explicit or implicit depend on specific conditions, as a rule they are local stability conditions for the cell. It is appreciably that not all variables in cell are considered explicitly because stability conditions apply to certain variable. Particularly, pore pressure evolution is described by parabolic equation so one must use implicit scheme to compute pore pressure. In addition, the problem of proper variable choice for filtration with phase transition processes description is also considered.