Application of multiscale algorithms for solving problems of multiphase flow in anisotropic media

In the paper, an effective multiscale multigrid algorithm of solving multiphase flow problems was developed to construct effective relative permeabilities for anisotropic media of complex structure. The method combines the Fedorenko finite superelement method and the Samarskii support operators method and belongs to the high-resolution methods class. The numerical simulation was carried out both for random distribution of permeability and for media with an arbitrary fractures configuration. The anisotropy of the relative permeabilities is shown as a consequence of the anisotropy of absolute permeability.