Geodesic
Spatial approximation by the subgrid method in the filtration problem for a viscous compressible fluid in a porous medium
Numerical methods and programming, Tome 9 (2008) no. 3, pp. 191-199.

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The filtration problem for a viscous compressible multiphase fluid mixture in an anisotropic porous medium is considered. For this problem, the spatial approximation is discussed in the case of nonorthogonal unstructured grids. A new method of multipoint approximation is proposed. This method is free from the following defects of other similar methods: the orientation effect and the appearance of nonphysical fluxes. Some numerical results obtained on the basis of realistic problems are given.
Keywords: linear systems, subgrid method, control-volume method, parallel computing.
Mots-clés : fluid filtration 
@article{VMP_2008_9_3_a1,
     author = {K. Yu. Bogachev and N. S. Melnichenko},
     title = {Spatial approximation by the subgrid method in the filtration problem for a viscous compressible fluid in a porous medium},
     journal = {Numerical methods and programming},
     pages = {191--199},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a1/}
}
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K. Yu. Bogachev; N. S. Melnichenko. Spatial approximation by the subgrid method in the filtration problem for a viscous compressible fluid in a porous medium. Numerical methods and programming, Tome 9 (2008) no. 3, pp. 191-199. http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a1/