A multilevel multiscale mimetic (M3) method for an anisotropic infiltration problem

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5544 LNCS, Issue PART 1, 2009, Pages 685-694

  Lipnikov, Konstantin ^a   Moulton, David ^a   Svyatskiy, Daniil ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Heterogeneous porous media; Hierarchical; Infiltration; Multiscale; Two phase flow

Indexed keywords

COORDINATE AXES; HETEROGENEOUS POROUS MEDIA; HIERARCHICAL; HIERARCHICAL APPROACH; LAYERED MEDIUM; MULTISCALE; MULTISCALES; TEMPORAL SCALE; TENSOR PERMEABILITY; TWO-DIMENSIONAL; TWO-PHASE FLOWS; UPDATING STRATEGY;

POROUS MATERIALS; SEEPAGE; SOIL MECHANICS; TWO PHASE FLOW;

FLUID DYNAMICS;

EID: 68949086486     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-01970-8_68     Document Type: Conference Paper

References (16)

1. 3) method for two-phase flows in porous media. J. Comput. Phys. 227, 6727-6753 (2008)
2. Hou, T.Y., Wu, X.H.: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134, 169-189 (1997)
3. Aarnes, J.E., Kippe, V., Lie, K.A.: Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Resour. 28, 257-271 (2005)
4. Hughes, T.J.: Multiscale phenomena: Green's functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering 127, 387-401 (1995)
5. Arbogast, T., Pencheva, G., Wheeler, M.F., Yotov, I.: A multiscale mortar mixed finite element method. Multiscale Model. Simul. 6, 319-346 (2007)
6. Jenny, P., Lee, S.H., Tchelepi, H.A.: Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput. Phys. 187, 47-67 (2003)
7. Kuznetsov, Y.A.: Mixed finite element method for diffusion equations on polygonal meshes with mixed cells. J. Numer. Math. 14, 305-315 (2006)
8. Lunati, I., Jenny, P.: Treating highly anisotropic subsurface flow with the multiscale finite-volume method. Multiscale Model. Sim. 6, 308-318 (2007)
9. Forsyth, P.A., Wu, Y.S., Pruess, K.: Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media. Adv. Water Resour. 18, 25-38 (1995)
10. Lunati, I., Jenny, P.: Multiscale finite-volume method for density-driven flow in porous media. Computat. Geosci. 12, 337-350 (2008)
11. Forsyth, P.: A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Stat. Comput. 12, 1029-1057 (1991)
12. Brezzi, F., Lipnikov, K., Simoncini, V.: A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Mod. Meth. Appl. S. 15, 1533-1551 (2005)
13. Jenny, P., Lee, S.H., Tchelepi, H.A.: Adaptive multiscale finite-volume method for multiphase flow and transport in porous media. Multiscale Model. Sim. 3, 50-64 (2004)
14. Ruge, J.W., Stüben, K.: Algebraic multigrid (AMG). In: McCormick, S.F. (ed.) Multigrid Methods. Frontiers in Applied Mathematics, vol. 3, pp. 73-130. SIAM, Philadelphia (1987)
15. Zyvoloski, G.A., Vesselinov, V.V.: An investigation of numerical grid effects in parameter estimation. Ground Water 44, 814-825 (2006)
16. Coats, K.H.: Impes stability: Selection of stable timesteps. SPE J 8, 181-187 (2003)