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Volumn 227, Issue 14, 2008, Pages 6727-6753

A multilevel multiscale mimetic (M3) method for two-phase flows in porous media

Author keywords

Algebraic multigrid method; Mimetic discretization; Multiscale methods; Porous media; Reservoir simulation; Two phase flow; Upscaling techniques

Indexed keywords

ALGEBRA; COARSENING; DIFFUSION; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; MAXWELL EQUATIONS; NUMERICAL METHODS; PETROLEUM RESERVOIR ENGINEERING; PETROLEUM RESERVOIRS; POROUS MATERIALS; RESERVOIRS (WATER);

EID: 44649161800     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.03.029     Document Type: Article
Times cited : (57)

References (31)
  • 1
    • 81255135476 scopus 로고    scopus 로고
    • On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation
    • Aarnes J.E. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model Simulat. 2 3 (2004) 421-439
    • (2004) Multiscale Model Simulat. , vol.2 , Issue.3 , pp. 421-439
    • Aarnes, J.E.1
  • 2
    • 13844298952 scopus 로고    scopus 로고
    • Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels
    • Aarnes J.E., Kippe V., and Lie K.-A. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Resour. 28 3 (2005) 257-271
    • (2005) Adv. Water Resour. , vol.28 , Issue.3 , pp. 257-271
    • Aarnes, J.E.1    Kippe, V.2    Lie, K.-A.3
  • 3
    • 0000828256 scopus 로고
    • Generalized finite element methods: their performance and their relation to mixed methods
    • Babuška I., and Osborn J.E. Generalized finite element methods: their performance and their relation to mixed methods. SIAM J. Numer. Anal. 20 3 (1983) 510-536
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.3 , pp. 510-536
    • Babuška, I.1    Osborn, J.E.2
  • 7
    • 34447101360 scopus 로고    scopus 로고
    • A new discretization methodology for diffusion problems on generalized polyhedral meshes
    • Brezzi F., Lipnikov K., Shashkov M., and Simoncini V. A new discretization methodology for diffusion problems on generalized polyhedral meshes. Comput. Method Appl. M. 196 37-40 (2007) 3682-3692
    • (2007) Comput. Method Appl. M. , vol.196 , Issue.37-40 , pp. 3682-3692
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3    Simoncini, V.4
  • 8
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • Brezzi F., Lipnikov K., and Simoncini V. A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Mod. Methods Appl. Syst. 15 10 (2005) 1533-1551
    • (2005) Math. Mod. Methods Appl. Syst. , vol.15 , Issue.10 , pp. 1533-1551
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 9
    • 0037376524 scopus 로고    scopus 로고
    • A mixed multiscale finite element method for elliptic problems with oscillating coefficients
    • Chen Z., and Hou T.Y. A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput. 72 242 (2003) 541-576
    • (2003) Math. Comput. , vol.72 , Issue.242 , pp. 541-576
    • Chen, Z.1    Hou, T.Y.2
  • 11
    • 0001677218 scopus 로고
    • Black box multigrid
    • Dendy J.E. Black box multigrid. J. Comput. Phys. 48 (1982) 366-386
    • (1982) J. Comput. Phys. , vol.48 , pp. 366-386
    • Dendy, J.E.1
  • 12
    • 0000025929 scopus 로고
    • Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients
    • Dendy J.E. Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients. SIAM J. Sci. Stat. Comput. 8 2 (1987) 673-685
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , Issue.2 , pp. 673-685
    • Dendy, J.E.1
  • 14
    • 33751252248 scopus 로고    scopus 로고
    • Accurate multiscale finite element methods for two-phase flow simulations
    • Efendiev Y., Ginting V., Hou T., and Ewing R. Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys. 220 1 (2006) 155-174
    • (2006) J. Comput. Phys. , vol.220 , Issue.1 , pp. 155-174
    • Efendiev, Y.1    Ginting, V.2    Hou, T.3    Ewing, R.4
  • 15
    • 0024863696 scopus 로고
    • Numerical simulation of gas venting for NAPL site remediation
    • Forsyth P.A. Numerical simulation of gas venting for NAPL site remediation. Soc. Pet. Eng. AIME Paper SPE 18415 (1989) 85-96
    • (1989) Soc. Pet. Eng. AIME Paper SPE , vol.18415 , pp. 85-96
    • Forsyth, P.A.1
  • 16
    • 0000370771 scopus 로고
    • A control volume finite element approach to NAPL groundwater contamination
    • Forsyth P.A. A control volume finite element approach to NAPL groundwater contamination. SIAM J. Scient. Statist. Comput. 12 5 (1991) 1029-1057
    • (1991) SIAM J. Scient. Statist. Comput. , vol.12 , Issue.5 , pp. 1029-1057
    • Forsyth, P.A.1
  • 17
    • 85189841466 scopus 로고    scopus 로고
    • V. Gvozdev, Discretization of the diffusion and Maxwell equations on polyhedral meshes, Technical Report Ph.D. Thesis, University of Houston, 2007.
    • V. Gvozdev, Discretization of the diffusion and Maxwell equations on polyhedral meshes, Technical Report Ph.D. Thesis, University of Houston, 2007.
  • 18
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou T.Y., and Wu X.H. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169-189
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.H.2
  • 19
    • 15744392935 scopus 로고    scopus 로고
    • Adaptive multiscale finite-volume method for multiphase flow and transport in porous media
    • September 2004; 2004-2005.
    • Jenny P., Lee S.H., and Tchelepi H.A. Adaptive multiscale finite-volume method for multiphase flow and transport in porous media. Multiscale Model. Simulat. 3 1 (2004) 50-64 September 2004; 2004-2005.
    • (2004) Multiscale Model. Simulat. , vol.3 , Issue.1 , pp. 50-64
    • Jenny, P.1    Lee, S.H.2    Tchelepi, H.A.3
  • 21
    • 85189838136 scopus 로고    scopus 로고
    • V. Kippe, J.E. Aarnes, K.-A. Lie. A comparison of multiscale methods for elliptic problems in porous media flow. Computat. Geosci., Special Issue on Multiscale Methods, 2008, doi:10.1007/s10596-007-9074-6.
    • V. Kippe, J.E. Aarnes, K.-A. Lie. A comparison of multiscale methods for elliptic problems in porous media flow. Computat. Geosci., Special Issue on Multiscale Methods, 2008, doi:10.1007/s10596-007-9074-6.
  • 22
    • 84962820631 scopus 로고    scopus 로고
    • Mixed finite element methods on polyhedral meshes for diffusion equations
    • Springer-Verlag, Berlin
    • Kuznetsov Yu. Mixed finite element methods on polyhedral meshes for diffusion equations. Computational Modeling with PDEs in Science and Engineering (2008), Springer-Verlag, Berlin
    • (2008) Computational Modeling with PDEs in Science and Engineering
    • Kuznetsov, Yu.1
  • 23
    • 33846251986 scopus 로고    scopus 로고
    • Mixed finite element method for diffusion equations on polygonal meshes with mixed cells
    • Kuznetsov Yu.A. Mixed finite element method for diffusion equations on polygonal meshes with mixed cells. J. Numer. Math. 14 4 (2006) 305-315
    • (2006) J. Numer. Math. , vol.14 , Issue.4 , pp. 305-315
    • Kuznetsov, Yu.A.1
  • 24
    • 33645748300 scopus 로고    scopus 로고
    • Multilevel upscaling through variational coarsening
    • MacLachlan S.P., and Moulton J.D. Multilevel upscaling through variational coarsening. Water Resour. Res. 42 (2006)
    • (2006) Water Resour. Res. , vol.42
    • MacLachlan, S.P.1    Moulton, J.D.2
  • 25
    • 0023208436 scopus 로고
    • Examination of the upwind (donor-cell) formulation in control volume finite-element methods for fluid flow and heat transfer
    • Prakash C. Examination of the upwind (donor-cell) formulation in control volume finite-element methods for fluid flow and heat transfer. Numer. Heat Transfer 11 4 (1987) 401-416
    • (1987) Numer. Heat Transfer , vol.11 , Issue.4 , pp. 401-416
    • Prakash, C.1
  • 26
    • 0001885411 scopus 로고
    • Algebraic multigrid (AMG)
    • Multigrid Methods. McCormick S.F. (Ed), SIAM, Philadelphia, PA
    • Ruge J.W., and Stüben K. Algebraic multigrid (AMG). In: McCormick S.F. (Ed). Multigrid Methods. Frontiers in Applied Mathematics vol. 3 (1987), SIAM, Philadelphia, PA 73-130
    • (1987) Frontiers in Applied Mathematics , vol.3 , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 27
    • 3242689474 scopus 로고    scopus 로고
    • p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems
    • Strouboulis T., Zhang L., and Babuška I. p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Int. J. Numer. Meth. Eng. 60 10 (2004) 1639-1672
    • (2004) Int. J. Numer. Meth. Eng. , vol.60 , Issue.10 , pp. 1639-1672
    • Strouboulis, T.1    Zhang, L.2    Babuška, I.3
  • 28
    • 0002621183 scopus 로고
    • Algebraic multigrid (AMG): experiences and comparisons
    • Stüben K. Algebraic multigrid (AMG): experiences and comparisons. Appl. Math. Comput. 13 (1983) 419-451
    • (1983) Appl. Math. Comput. , vol.13 , pp. 419-451
    • Stüben, K.1
  • 29
    • 0035282142 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • Stüben K. A review of algebraic multigrid. J. Comput. Appl. Math. 128 1-2 (2001) 281-309
    • (2001) J. Comput. Appl. Math. , vol.128 , Issue.1-2 , pp. 281-309
    • Stüben, K.1
  • 30
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • Vanek P., Mandel J., and Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56 3 (1996) 179-196
    • (1996) Computing , vol.56 , Issue.3 , pp. 179-196
    • Vanek, P.1    Mandel, J.2    Brezina, M.3
  • 31
    • 44649145369 scopus 로고
    • A finite element synthesis method
    • Yang S.-t., and Henry A.F. A finite element synthesis method. Nucl. Sci. Eng. 59 1 (1976) 63-67
    • (1976) Nucl. Sci. Eng. , vol.59 , Issue.1 , pp. 63-67
    • Yang, S.-t.1    Henry, A.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.