Numerical Analysis
Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1007-1012.

This Note proves the convergence of the finite volume MultiPoint Flux Approximation (MPFA) O scheme for anisotropic and heterogeneous diffusion problems. Its main originality is that our framework and proof deal with general polygonal and polyhedral meshes as well as with L diffusion coefficients, which is essential in practical applications.

Cette Note démontre la convergence du schéma volume fini de type « O » pour les problèmes de diffusion en milieu hétérogène anisotrope. Sa principale originalité est de traiter des maillages polygonaux et polyédriques généraux ainsi que des coefficients de diffusion L, ce qui est essentiel dans les applications.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.015
Agelas, Leo 1; Masson, Roland 1

1 Institut français du petrole, Division technologie, information, 1 et 4, avenue de Bois Préau, 92852 Rueil Malmaison, France
@article{CRMATH_2008__346_17-18_1007_0,
     author = {Agelas, Leo and Masson, Roland},
     title = {Convergence of the finite volume {MPFA} {O} scheme for heterogeneous anisotropic diffusion problems on general meshes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1007--1012},
     publisher = {Elsevier},
     volume = {346},
     number = {17-18},
     year = {2008},
     doi = {10.1016/j.crma.2008.07.015},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.07.015/}
}
TY  - JOUR
AU  - Agelas, Leo
AU  - Masson, Roland
TI  - Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 1007
EP  - 1012
VL  - 346
IS  - 17-18
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.07.015/
DO  - 10.1016/j.crma.2008.07.015
LA  - en
ID  - CRMATH_2008__346_17-18_1007_0
ER  - 
%0 Journal Article
%A Agelas, Leo
%A Masson, Roland
%T Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes
%J Comptes Rendus. Mathématique
%D 2008
%P 1007-1012
%V 346
%N 17-18
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.07.015/
%R 10.1016/j.crma.2008.07.015
%G en
%F CRMATH_2008__346_17-18_1007_0
Agelas, Leo; Masson, Roland. Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 1007-1012. doi : 10.1016/j.crma.2008.07.015. http://www.numdam.org/articles/10.1016/j.crma.2008.07.015/

[1] Aavatsmark, I. An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci., Volume 6 (2002), pp. 405-432

[2] Aavatsmark, I.; Eigestad, G.T.; Klausen, R.A.; Wheeler, M.F.; Yotov, I. Convergence of a symmetric MPFA method on quadrilateral grids, Comput. Geosci., Volume 11 (2007), pp. 333-345

[3] L. Agelas, D. Di Pietro, R. Masson, A symmetric finite volume scheme for multiphase porous media flow problems with applications in the oil industry, in: Proceedings of the Finite Volume for Complex Applications Conference, June 8–13, 2008

[4] L. Agelas, R. Masson, Convergence of finite volume MPFA O type schemes for heterogeneous anisotropic diffusion problems on general meshes, Numer. Math. 5981 (2008), submitted for publication

[5] Breil, J.; Maire, P.H. A cell-centered diffusion scheme on two dimensional unstructured meshes, J. Comput. Phys., Volume 224 (2007) no. 2, pp. 785-823

[6] Edwards, M.G. Unstructured control-volume distributed full tensor finite volume schemes with flow based grids, Comput. Geosci., Volume 6 (2002), pp. 433-452

[7] Eymard, R.; Gallouët, T.; Herbin, R. A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis, C. R. Acad. Sci. Paris, Ser. I, Volume 344 (2007) no. 6, pp. 403-406

[8] Eymard, R.; Herbin, R. A new colocated finite volume scheme for the incompressible Navier–Stokes equations on general non matching grids, C. R. Acad. Sci. Paris, Ser. I, Volume 344 (2007) no. 10, pp. 659-662

[9] D. Gunasekera, P. Childs, J. Herring, J. Cox, A multi-point flux discretization scheme for general polyhedral grids, SPE 48855, in: Proc. SPE 6th International Oil and Gas Conference and Exhibition, China, November 1998

[10] Klausen, R.A.; Winther, R. Robust convergence of multi point flux approximation on rough grids, Numer. Math., Volume 104 (2006) no. 3, pp. 317-337

[11] Klausen, R.A.; Winther, R. Convergence of multi-point flux approximations on quadrilateral grids, Numer. Methods Partial Differential Equations, Volume 22 (2006) no. 6, pp. 1438-1454

[12] Le Potier, C. Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés, C. R. Acad. Sci. Paris, Ser. I, Volume 340 (2005), pp. 921-926

[13] K. Lipnikov, M. Shashkov, I. Yotov, Local flux mimetic finite difference methods, Technical report LA-UR-05-8364, Los Alamos National Laboratory, 2005

Cited by Sources: