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Volumn 136, Issue 2, 1997, Pages 522-545

Adaptive mesh refinement and multilevel iteration for flow in porous media

Author keywords

[No Author keywords available]

Indexed keywords

GAS DYNAMICS; INCOMPRESSIBLE FLOW; INFORMATION MANAGEMENT; ITERATIVE METHODS; MESH GENERATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; OBJECT ORIENTED PROGRAMMING; POROUS MATERIALS;

EID: 0031572117     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5779     Document Type: Article
Times cited : (77)

References (87)
  • 1
    • 84968500702 scopus 로고
    • On the implementation of mixed methods as nonconforming methods for second-order elliptic problems
    • Abrogast T. J., Chen Z. On the implementation of mixed methods as nonconforming methods for second-order elliptic problems. Math. Comp. 64:1995;943.
    • (1995) Math. Comp. , vol.64 , pp. 943
    • Abrogast, T.J.1    Chen, Z.2
  • 2
    • 0000014842 scopus 로고
    • The multi-grid method for the diffusion equation with strongly discontinuous coefficients
    • Alcouffe R. E., Brandt A., Dendy J. E., Painter J. The multi-grid method for the diffusion equation with strongly discontinuous coefficients. SIAM J. Sci. Stat. Comp. 2:1981;430.
    • (1981) SIAM J. Sci. Stat. Comp. , vol.2 , pp. 430
    • Alcouffe, R.E.1    Brandt, A.2    Dendy, J.E.3    Painter, J.4
  • 3
    • 0001705515 scopus 로고
    • Well-conditioned iterative schemes for mixed finite-element models of porous media flows
    • Allen M. B., Ewing R. E., Lu P. Well-conditioned iterative schemes for mixed finite-element models of porous media flows. SIAM J. Sci. Stat. Comp. 13:1992;794.
    • (1992) SIAM J. Sci. Stat. Comp. , vol.13 , pp. 794
    • Allen, M.B.1    Ewing, R.E.2    Lu, P.3
  • 4
    • 0003499489 scopus 로고
    • Multi-Phase Flow in Porous Media: Mechanics, Mathematics and Numerics
    • New York/Berlin: Springer-Verlag
    • Allen M. B. III, Behie A., Trangenstein J. A. Multi-Phase Flow in Porous Media: Mechanics, Mathematics and Numerics. Lecture Notes in Engineering. 34:1988;Springer-Verlag, New York/Berlin.
    • (1988) Lecture Notes in Engineering , vol.34
    • Allen M.B. III1    Behie, A.2    Trangenstein, J.A.3
  • 7
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: Implementation, postprocessing, and error estimates
    • Arnold D. N., Brezzi F. Mixed and nonconforming finite element methods: Implementation, postprocessing, and error estimates. RAIRO Modél. Math. Anal. Numér. 19:1985;7.
    • (1985) RAIRO Modél. Math. Anal. Numér. , vol.19 , pp. 7
    • Arnold, D.N.1    Brezzi, F.2
  • 8
    • 0004002971 scopus 로고
    • Petroleum Reservoir Simulation
    • Essex: Braking
    • Aziz K., Settari A. Petroleum Reservoir Simulation. Appl. Sci. 1979;Braking, Essex.
    • (1979) Appl. Sci.
    • Aziz, K.1    Settari, A.2
  • 10
    • 0000494892 scopus 로고
    • Higher-order Godunov methods for general systems of hyperbolic conservation laws
    • Bell J. B., Colella P., Transgenstein J. A. Higher-order Godunov methods for general systems of hyperbolic conservation laws. J. Comp. Phys. 82:1989;362.
    • (1989) J. Comp. Phys. , vol.82 , pp. 362
    • Bell, J.B.1    Colella, P.2    Transgenstein, J.A.3
  • 11
    • 33749535785 scopus 로고
    • An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
    • Bell J. B., Dawson C. N., Shubin G. R. An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions. J. Comp. Phys. 74:1988;1.
    • (1988) J. Comp. Phys. , vol.74 , pp. 1
    • Bell, J.B.1    Dawson, C.N.2    Shubin, G.R.3
  • 12
    • 38249040048 scopus 로고
    • A method for reducing numerical dispersion in two-phase black-oil reservoir simulation
    • Bell J. B., Shubin G. R., Trangenstein J. A. A method for reducing numerical dispersion in two-phase black-oil reservoir simulation. J. Comp. Phys. 65:1986;71.
    • (1986) J. Comp. Phys. , vol.65 , pp. 71
    • Bell, J.B.1    Shubin, G.R.2    Trangenstein, J.A.3
  • 13
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • Berger M. J., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1989;64.
    • (1989) J. Comput. Phys. , vol.82 , pp. 64
    • Berger, M.J.1    Colella, P.2
  • 15
    • 48749141209 scopus 로고
    • Adaptive mesh refinement for hyperbolic partial differential equations
    • Berger M. J., Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comp. Phys. 53:1984;484.
    • (1984) J. Comp. Phys. , vol.53 , pp. 484
    • Berger, M.J.1    Oliger, J.2
  • 16
    • 84966238014 scopus 로고
    • An iterative method for elliptic problems on regions partitioned into substructures
    • Bramble J. H., Pasciak J. E., Schatz A. H. An iterative method for elliptic problems on regions partitioned into substructures. Math. Comp. 46:1986;361.
    • (1986) Math. Comp. , vol.46 , pp. 361
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 17
    • 84966251372 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, ii
    • Bramble J. H., Pasciak J. E., Schatz A. H. The construction of preconditioners for elliptic problems by substructuring, ii. Math. Comp. 49:1987;1.
    • (1987) Math. Comp. , vol.49 , pp. 1
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 18
    • 84966211313 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, iii
    • Bramble J. H., Pasciak J. E., Schatz A. H. The construction of preconditioners for elliptic problems by substructuring, iii. Math. Comp. 51:1988;415.
    • (1988) Math. Comp. , vol.51 , pp. 415
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 19
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • Bramble J. H., Pasciak J. E., Wang J., Xu J. Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comp. 57:1991;23.
    • (1991) Math. Comp. , vol.57 , pp. 23
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 20
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • Brandt A. Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31:1977;333.
    • (1977) Math. Comp. , vol.31 , pp. 333
    • Brandt, A.1
  • 21
    • 0010875153 scopus 로고
    • On the stability of pressure and velocity computations for heterogeneous reservoirs
    • Bruaset A. M., Nielsen B. F. On the stability of pressure and velocity computations for heterogeneous reservoirs. Technical report. 1994.
    • (1994) Technical Report
    • Bruaset, A.M.1    Nielsen, B.F.2
  • 22
    • 26844455510 scopus 로고
    • Multidimensional unsplit methods for hyperbolic conservation laws
    • Colella P. Multidimensional unsplit methods for hyperbolic conservation laws. J. Comp. Phys. 87:1990;171.
    • (1990) J. Comp. Phys. , vol.87 , pp. 171
    • Colella, P.1
  • 23
    • 30244574916 scopus 로고
    • Parallel adaptive mesh refinement: An example of parallel data encapsulation
    • Crutchfield W. Y. Parallel adaptive mesh refinement: An example of parallel data encapsulation. LLNL report. UCRL-JC-107680:1991.
    • (1991) LLNL Report. UCRL-JC-107680
    • Crutchfield, W.Y.1
  • 26
    • 0026865997 scopus 로고
    • Characteristic, local grid refinement techniques for reservoir flow problems
    • Dahle H. K., Espedal M. S., Sævereid O. Characteristic, local grid refinement techniques for reservoir flow problems. Inter. J. Numer. Engrg. 34:1992;1051.
    • (1992) Inter. J. Numer. Engrg. , vol.34 , pp. 1051
    • Dahle, H.K.1    Espedal, M.S.2    Sævereid, O.3
  • 27
    • 0010875412 scopus 로고    scopus 로고
    • Parallel adaptive hp-refinement techniques for conservation laws
    • Devine K. D., Flaherty J. E. Parallel adaptive hp-refinement techniques for conservation laws. Appl. Numer. Maths. 16:1996;1.
    • (1996) Appl. Numer. Maths. , vol.16 , pp. 1
    • Devine, K.D.1    Flaherty, J.E.2
  • 28
    • 0002329650 scopus 로고
    • The approximation of the pressure by a mixed method in the simulation of miscible displacement
    • Douglas J., Ewing R. E., Wheeler M. F. The approximation of the pressure by a mixed method in the simulation of miscible displacement. RAIRO Anal. Num. 17:1983;17.
    • (1983) RAIRO Anal. Num. , vol.17 , pp. 17
    • Douglas, J.1    Ewing, R.E.2    Wheeler, M.F.3
  • 32
    • 84966249747 scopus 로고
    • Local refinement techniques for elliptic problems on cell-centered grids i: Error analysis
    • Ewing R. E., Lazarov R. D., Vassilevski P. S. Local refinement techniques for elliptic problems on cell-centered grids i: Error analysis. Math. Comp. 56:1991;437.
    • (1991) Math. Comp. , vol.56 , pp. 437
    • Ewing, R.E.1    Lazarov, R.D.2    Vassilevski, P.S.3
  • 33
    • 0026203036 scopus 로고
    • Superconvergence of the velocity along the gauss lines in mixed finite element methods
    • Ewing R. E., Lazarov R. D., Wang J. Superconvergence of the velocity along the gauss lines in mixed finite element methods. SIAM J. Num. Anal. 28:1991;1015.
    • (1991) SIAM J. Num. Anal. , vol.28 , pp. 1015
    • Ewing, R.E.1    Lazarov, R.D.2    Wang, J.3
  • 34
    • 21144467527 scopus 로고
    • Analysis of mixed finite element methods on locally refined grids
    • Wing R. E., Wang J. Analysis of mixed finite element methods on locally refined grids. Numer. Math. 63:1992;183.
    • (1992) Numer. Math. , vol.63 , pp. 183
    • Wing, R.E.1    Wang, J.2
  • 37
    • 0000935266 scopus 로고
    • Difference methods for the numerical calculation of the equations of fluid dynamics
    • Godunov S. K. Difference methods for the numerical calculation of the equations of fluid dynamics. Mat. Sb. 47:1959;271.
    • (1959) Mat. Sb. , vol.47 , pp. 271
    • Godunov, S.K.1
  • 38
    • 0003815501 scopus 로고
    • Multi-Grid Methods and Applications
    • New York/Berlin: Springer-Verlag
    • Hackbusch W. Multi-Grid Methods and Applications. Comput. Math. 4:1985;Springer-Verlag, New York/Berlin.
    • (1985) Comput. Math. , vol.4
    • Hackbusch, W.1
  • 49
    • 0000226931 scopus 로고
    • The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding
    • Johansen T., Winther R. The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM J. Math. Anal. 19:1988;541.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 541
    • Johansen, T.1    Winther, R.2
  • 50
    • 0010809858 scopus 로고
    • The Riemann problem for multicomponent polymer flooding
    • Johansen T., Winther R. The Riemann problem for multicomponent polymer flooding. SIAM J. Math. Anal. 20:1989;909.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 909
    • Johansen, T.1    Winther, R.2
  • 52
    • 0000876881 scopus 로고
    • Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods
    • Springer-Verlag. p. 502-
    • Kettler R. Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods. Proceedings of the Conference on Multigrid Methods. Lecture Notes in Mathematics. 960:1982;Springer-Verlag. p. 502-.
    • (1982) Proceedings of the Conference on Multigrid Methods Lecture Notes in Mathematics , vol.960
    • Kettler, R.1
  • 54
    • 0003049981 scopus 로고
    • Vertex-centered and cell-centered multigrid for interface problems
    • Khalil M., Wesseling P. Vertex-centered and cell-centered multigrid for interface problems. J. Comp. Phys. 1992;1.
    • (1992) J. Comp. Phys. , pp. 1
    • Khalil, M.1    Wesseling, P.2
  • 57
    • 0003671760 scopus 로고
    • Numerical Methods for Conservation Laws
    • Basel: Birkhäuser
    • LeVeque R. J. Numerical Methods for Conservation Laws. Lectures in Mathematics. 1990;Birkhäuser, Basel.
    • (1990) Lectures in Mathematics
    • LeVeque, R.J.1
  • 61
    • 0003816338 scopus 로고
    • Multilevel Adaptive Methods for Partial Differential Equations
    • Philadelphia: SIAM
    • McCormick S. F. Multilevel Adaptive Methods for Partial Differential Equations. Frontiers in Applied Mathematics. 6:1989;SIAM, Philadelphia.
    • (1989) Frontiers in Applied Mathematics , vol.6
    • McCormick, S.F.1
  • 63
    • 0022144821 scopus 로고
    • Convergence of generalized MUSCL schemes
    • Osher S. Convergence of generalized MUSCL schemes. SIAM J. Num. Anal. 22:1985;947.
    • (1985) SIAM J. Num. Anal. , vol.22 , pp. 947
    • Osher, S.1
  • 65
    • 0019030466 scopus 로고
    • The application of fractional flow theory to enhanced oil recovery
    • Pope G. A. The application of fractional flow theory to enhanced oil recovery. Society of Petroleum Engineers J. 20:1980;191.
    • (1980) Society of Petroleum Engineers J. , vol.20 , pp. 191
    • Pope, G.A.1
  • 67
    • 0003588929 scopus 로고
    • Mathematical and Computational Techniques for Multilevel Adaptive Methods
    • SIAM
    • Rüde U. Mathematical and Computational Techniques for Multilevel Adaptive Methods. Frontiers in Applied Mathematics. 13:1993;SIAM.
    • (1993) Frontiers in Applied Mathematics , vol.13
    • Rüde, U.1
  • 68
    • 0001328401 scopus 로고
    • The calculation of the interaction of non-stationary shock waves with barriers
    • Rusanov V. V. The calculation of the interaction of non-stationary shock waves with barriers. J. Comp. Math. Math. Phys. USSR. 1:1961;267.
    • (1961) J. Comp. Math. Math. Phys. USSR , vol.1 , pp. 267
    • Rusanov, V.V.1
  • 69
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • R.E. Ewing. Society for Industrial and Applied Mathematics
    • Russell T. F., Wheeler M. F. Finite element and finite difference methods for continuous flows in porous media. Ewing R. E. The Mathematics of Reservoir Simulation. 1983;35 Society for Industrial and Applied Mathematics.
    • (1983) The Mathematics of Reservoir Simulation , pp. 35
    • Russell, T.F.1    Wheeler, M.F.2
  • 70
  • 71
    • 0002232239 scopus 로고
    • Adaptive local grid refinement and multi-grid in numerical reservoir simulation
    • Schmidt G. H., Jacobs F. J. Adaptive local grid refinement and multi-grid in numerical reservoir simulation. J. Comp. Phys. 77:1988;140.
    • (1988) J. Comp. Phys. , vol.77 , pp. 140
    • Schmidt, G.H.1    Jacobs, F.J.2
  • 72
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes ii
    • Shu C. W., Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes ii. J. Comp. Phys. 83:1989;32.
    • (1989) J. Comp. Phys. , vol.83 , pp. 32
    • Shu, C.W.1    Osher, S.2
  • 73
    • 0021594353 scopus 로고
    • An analysis of the grid orientation effect in numerical simulation of miscible displacement
    • Shubin G. R., Bell J. B. An analysis of the grid orientation effect in numerical simulation of miscible displacement. Comput. Meth. in Appl. Mech. and Engr. 47:1984;47.
    • (1984) Comput. Meth. in Appl. Mech. and Engr. , vol.47 , pp. 47
    • Shubin, G.R.1    Bell, J.B.2
  • 75
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • Sweby P. K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Num. Anal. 21:1984;995.
    • (1984) SIAM J. Num. Anal. , vol.21 , pp. 995
    • Sweby, P.K.1
  • 76
    • 0028375704 scopus 로고
    • A second-order Godunov algorithm for two-dimensional solid mechanics
    • Trangenstein J. A. A second-order Godunov algorithm for two-dimensional solid mechanics. Comput. Mech. 13:1994;343.
    • (1994) Comput. Mech. , vol.13 , pp. 343
    • Trangenstein, J.A.1
  • 77
    • 0001049122 scopus 로고
    • Adaptive mesh refinement for wave propagation in nonlinear solids
    • Trangenstein J. A. Adaptive mesh refinement for wave propagation in nonlinear solids. SIAM J. Sci. Stat. Comput. 16:1995;819.
    • (1995) SIAM J. Sci. Stat. Comput. , vol.16 , pp. 819
    • Trangenstein, J.A.1
  • 78
    • 0010928302 scopus 로고
    • Mathematical structure of compositional reservoir simulation
    • Trangenstein J. A., Bell J. B. Mathematical structure of compositional reservoir simulation. SIAM J. Sci. Stat. Comput. 10:1989;817.
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , pp. 817
    • Trangenstein, J.A.1    Bell, J.B.2
  • 79
    • 0000010230 scopus 로고
    • Mathematical structure of the black-oil model for petroleum reservoir simulation
    • Trangenstein J. A., Bell J. B. Mathematical structure of the black-oil model for petroleum reservoir simulation. SIAM J. Appl. Math. 49:1989;749.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 749
    • Trangenstein, J.A.1    Bell, J.B.2
  • 80
    • 0002406348 scopus 로고
    • Numerical algorithms for strong discontinuities in elastic-plastic solids
    • Trangenstein J. A., Pember R. B. Numerical algorithms for strong discontinuities in elastic-plastic solids. J. Comp. Phys. 103:1992;63.
    • (1992) J. Comp. Phys. , vol.103 , pp. 63
    • Trangenstein, J.A.1    Pember, R.B.2
  • 81
    • 0000814788 scopus 로고
    • The solution of nonstrictly hyperbolic conservation laws may be hard to compute
    • Tveito A., Winther R. The solution of nonstrictly hyperbolic conservation laws may be hard to compute. SIAM J. Sci. Stat. Comput. 16:1995;320.
    • (1995) SIAM J. Sci. Stat. Comput. , vol.16 , pp. 320
    • Tveito, A.1    Winther, R.2
  • 82
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
    • van Leer B. Towards the ultimate conservative difference scheme. V. a second-order sequel to Godunov's method. J. Comp. Phys. 32:1979;101.
    • (1979) J. Comp. Phys. , vol.32 , pp. 101
    • Van Leer, B.1
  • 84
    • 0001669414 scopus 로고
    • On the convergence of block-centered finite differences for elliptic problems
    • Weiser A., Wheeler M. F. On the convergence of block-centered finite differences for elliptic problems. SIAM J. Num. Anal. 25:1988;351.
    • (1988) SIAM J. Num. Anal. , vol.25 , pp. 351
    • Weiser, A.1    Wheeler, M.F.2
  • 85
    • 38249027511 scopus 로고
    • Cell-centered multigrid for interface problems
    • Wesseling P. Cell-centered multigrid for interface problems. J. Comp. Phys. 79:1988;85.
    • (1988) J. Comp. Phys. , vol.79 , pp. 85
    • Wesseling, P.1


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