Geodesic
On some multiscale algorithms for sector modeling in multiphase flow problems
Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 3-17

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The multiscale algorithm for multiphase filtration problem is proposed. Filtration fluxes on the fine grid are determined from solution of the pressure equation on the coarse grid. Further, domain is decomposed on to subdomains with reasonable number of cells and the full second boundary condition filtration problem is solved using pressure equation. The support operator method has been improved for complex structure cell for solution of the pressure equation on the coarse grid. This method is high resolution one: i.e. it allows revealing solution properties related to fine grid structure.
Keywords: multiphase flows, approximation on the non-ortogonal grids, multiscale algorithms. 
@article{MM_2010_22_11_a0,
     author = {A. Kh. Pergament and V. A. Semiletov and P. Yu. Tomin},
     title = {On some multiscale algorithms for sector modeling in multiphase flow problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {22},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_11_a0/}
}
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A. Kh. Pergament; V. A. Semiletov; P. Yu. Tomin. On some multiscale algorithms for sector modeling in multiphase flow problems. Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2010_22_11_a0/