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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - K. D. Nikitin
TI  - Nonlinear finite volume method for two-phase flow in porous media
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 131
EP  - 147
VL  - 22
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_11_a10/
LA  - ru
ID  - MM_2010_22_11_a10
ER  - 
%0 Journal Article
%A K. D. Nikitin
%T Nonlinear finite volume method for two-phase flow in porous media
%J Matematičeskoe modelirovanie
%D 2010
%P 131-147
%V 22
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_11_a10/
%G ru
%F MM_2010_22_11_a10
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/

[1] Aziz K., Settari A., Petroleum Reservoir Simulation, Applied Sci. Publ. Ltd, London, 1979, 497 pp.

[2] Peaceman D. W., Fundamentals of Numerical Reservoir Simulation, Elsevier, New York, 1977, 176 pp.

[3] Chen Z., Huan G., Ma Y., Computational Methods for Multiphase Flows in Porous Media, SIAM, 2006, 549 pp. | MR

[4] Kanevskaya R. D., Matematicheskoe modelirovanie gidrodinamicheskikh protsessov razrabotki mestorozhdenii uglevodorodov, Moskva–Izhevsk, 2003, 128 pp.

[5] Sukhinov A. A., Matematicheskoe modelirovanie protsessov perenosa primesei v zhidkostyakh i poristykh sredakh, kandidatskaya dissertatsiya, 2009

[6] Eymard R., Gallouët T., Herbin R., “Finite Volume Methods”, Handbook of Numerical Analysis, 2000, 713–1020 | MR | Zbl

[7] Le Potier C., “Schema volumes finis monotone pour des operateurs de diffusion fortement anisotropes sur des maillages de triangle non structures”, C. R. Math. Acad. Sci. Paris, 341 (2005), 787–792 | MR | Zbl

[8] Lipnikov K., Svyatskiy D., Shashkov M., Vassilevski Yu., “Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes”, J. Comp. Phys., 227 (2007), 492–512 | DOI | MR | Zbl

[9] Lipnikov K., Svyatskiy D., Vassilevski Yu., “Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes”, J. Comp. Phys., 228 (2009), 703–716 | DOI | MR | Zbl

[10] Danilov A., Vassilevski Yu., “A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes”, Russian J. Numer. Anal. Math. Modelling, 24:3 (2009), 207–227 | DOI | MR | Zbl

[11] Aavatsmark I., Eigestad G. T., Mallison B. T., Nordbotten J. M., “A compact multipoint flux approximation method with improved robustness”, Numer. Methods for Partial Diff. Equations, 24:5 (2008), 1329–1360 | DOI | MR | Zbl

[12] Peaceman D. W., “Interpretation of Well-Block Pressures in Numerical Reservoir Simulation”, SPEJ, 1978, June, 183–194

[13] Kaporin I. E., “High quality preconditioning of a general symmetric positive matrix based on its $U^TU+U^TR+R^TU$-decomposition”, Num. Linear Algebra with Applications, 5 (1998), 484–509 | MR