The averaging algorithms for Lebedev’s grids and for non-orthogonal grids by the Samarskii support operator method are considered in the article. The averaging process allows integrating the grid cells in case the approximate solutions in the integrated cell may be determined. The functions describing the features of solutions have been obtained for integrated cells of the Lebedev and arbitrary non-orthogonal grids. It results from approximating fluxes in each cell for linear span elements of the functions mentioned above that the symmetric permeability tensor may be constructed and the flux approximation of the first order may be obtained. The flux approximation leads to the strong convergence of the algorithm. It is essential the system grid cells may be multiscale, i.e. sizes of cells and the values of permeabilities may be very different.<br><br>The flux approximation distinguishes this article results from those of other authors of averaging algorithms. Then the methods of flow modeling in anisotropic media have been developed.<br>


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