Geodesic
Nonlinear finite volume method for two-phase flow in porous media
Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 131-147

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The new finite volume method with nonlinear two-point flux discretization is being studied. We present an application of the method for two-phase flow model and conduct a comparison study of two approaches to discretization of the diffusive flux: conventional linear and proposed nonlinear two-point stencils. New method shows a number of important advantages over traditional approach, such as very low sensitivity to grid distortions and second order approximation in the case of full anisotropic diffusion tensor.
Keywords: two-phase flow model, finite volume method, two-point flux discretization, unstructured polyhedral mesh. 
@article{MM_2010_22_11_a10,
     author = {K. D. Nikitin},
     title = {Nonlinear finite volume method for two-phase flow in porous media},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {131--147},
     publisher = {mathdoc},
     volume = {22},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_11_a10/}
}
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K. D. Nikitin. Nonlinear finite volume method for two-phase flow in porous media. Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 131-147. http://geodesic.mathdoc.fr/item/MM_2010_22_11_a10/