A multiscale algorithm for a multiphase filtration problem is proposed.
Filtration fluxes on a fine grid are determined from the solution
of the pressure equation on a coarse grid. Further, the domain is
decomposed into subdomains with an acceptable number of cells and
the full second boundary condition filtration problem is solved using
the fluxes. The support operator method has been improved for a complex
structure cell for solution of the pressure equation on a coarse
grid. This method is a high resolution one: a divergence operator
has the approximation of the second order, while fluxes have the
approximation of the first order. At the same time, the method allows
revealing the solution's properties related to a fine grid structure.