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Volumn 12, Issue 4, 2008, Pages 525-539

A space-time discontinuous Galerkin method applied to single-phase flow in porous media

Author keywords

Convection dominant flow; Discontinuous Galerkin methods; Porous media

Indexed keywords

FINITE ELEMENT METHOD; FLOW OF FLUIDS; GALERKIN METHODS; POROUS MATERIALS;

EID: 56449109996     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-008-9092-z     Document Type: Article
Times cited : (12)

References (40)
  • 1
    • 0344315183 scopus 로고
    • Simulation of miscible displacement using mixed methods and a modified method of characteristics
    • Ewing, R.E., Wyoming, U., Russell, T.F., Wheeler, M.F.: Simulation of miscible displacement using mixed methods and a modified method of characteristics. Soc. Pet. Eng. J. 12241 (1983)
    • (1983) Soc. Pet. Eng. J. , pp. 12241
    • Ewing, R.E.1    Wyoming, U.2    Russell, T.F.3    Wheeler, M.F.4
  • 2
    • 0008065601 scopus 로고
    • The numerical simulation of miscible displacement in porous media
    • In: Oden, J.T. (ed.) North-Holland, Amsterdam
    • Douglas, J.: The numerical simulation of miscible displacement in porous media. In: Oden, J.T. (ed.) Computational Methods in Nonlinear Mechanics, pp. 225-237. North-Holland, Amsterdam (1980)
    • (1980) Computational Methods in Nonlinear Mechanics , pp. 225-237
    • Douglas, J.1
  • 3
    • 0000279634 scopus 로고
    • A method for predicting the performance of unstable miscible displacement in heterogeneous media
    • Koval, E.J.: A method for predicting the performance of unstable miscible displacement in heterogeneous media. Soc. Pet. Eng. J. 3, 145-154 (1963)
    • (1963) Soc. Pet. Eng. J. , vol.3 , pp. 145-154
    • Koval, E.J.1
  • 4
    • 33846524895 scopus 로고    scopus 로고
    • Adaptive simulations of two-phase flow by discontinuous Galerkin methods
    • Klieber, W., Rivière, B.: Adaptive simulations of two-phase flow by discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 196, 404-419 (2006)
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.196 , pp. 404-419
    • Klieber, W.1    Rivière, B.2
  • 5
    • 33748279485 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for flow and transport problems in porous media
    • Rivière, B., Wheeler, M.F.: Discontinuous Galerkin methods for flow and transport problems in porous media. Commun. Numer. Methods Eng. 79, 157-174 (2002)
    • (2002) Commun. Numer. Methods Eng. , vol.79 , pp. 157-174
    • Rivière, B.1    Wheeler, M.F.2
  • 6
    • 0343831462 scopus 로고    scopus 로고
    • Part II: Discontinuous Galerkin methods applied to a single phase flow in porous media
    • Rivière, B., Wheeler, M.F., Banaś, K.: Part II: Discontinuous Galerkin methods applied to a single phase flow in porous media. Comput. Geosci. 4, 337-349 (2000)
    • (2000) Comput. Geosci. , vol.4 , pp. 337-349
    • Rivière, B.1    Wheeler, M.F.2    Banaś, K.3
  • 7
    • 2542557493 scopus 로고    scopus 로고
    • Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements
    • Nayagum, D., Schäfer, G., Mosé, R.: Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements. Comput. Geotech. 8, 49-73 (2004)
    • (2004) Comput. Geotech. , vol.8 , pp. 49-73
    • Nayagum, D.1    Schäfer, G.2    Mosé, R.3
  • 8
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • Oden, J.T., Babuška, I., Baumann, C.E.: A discontinuous hp finite element method for diffusion problems. J. Chem. Phys. 146, 491-519 (1998)
    • (1998) J. Chem. Phys. , vol.146 , pp. 491-519
    • Oden, J.T.1    Babuška, I.2    Baumann, C.E.3
  • 9
    • 0033511173 scopus 로고    scopus 로고
    • Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I
    • Rivière, B., Wheeler, M.F., Girault, V.: Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Comput. Geosci. 3, 337-360 (1999)
    • (1999) Comput. Geosci. , vol.3 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 10
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • Wheeler, M.F.: An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15, 152-161 (1978)
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1
  • 11
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold, D.N.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19, 742-760 (1982)
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 12
    • 0347930482 scopus 로고    scopus 로고
    • Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations
    • Dawson, C., Proft, J.: Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations. Comput. Methods Appl. Mech. Eng. 193, 289-318 (2004)
    • (2004) Comput. Methods Appl. Mech. Eng. , vol.193 , pp. 289-318
    • Dawson, C.1    Proft, J.2
  • 13
    • 33644499155 scopus 로고    scopus 로고
    • Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media
    • Sun, S., Wheeler, M.F.: Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media. SIAM J. Numer. Anal. 43 (1), 195-219 (2005)
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.1 , pp. 195-219
    • Sun, S.1    Wheeler, M.F.2
  • 14
    • 10444236314 scopus 로고    scopus 로고
    • Compatible algorithms for coupled flow and transport
    • Dawson, C., Sun, S., Wheeler, M.: Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Eng. 193, 2565-2680 (2004)
    • (2004) Comput. Methods Appl. Mech. Eng. , vol.193 , pp. 2565-2680
    • Dawson, C.1    Sun, S.2    Wheeler, M.3
  • 17
    • 0014550435 scopus 로고
    • Finite elements in space and time
    • Argyris, J.H., Scharpf, D.W.: Finite elements in space and time. Nucl. Eng. Des. 10, 456-464 (1969)
    • (1969) Nucl. Eng. Des. , vol.10 , pp. 456-464
    • Argyris, J.H.1    Scharpf, D.W.2
  • 18
    • 85007700819 scopus 로고
    • Finite element analysis of time-dependent phenomena
    • Fried, I.: Finite element analysis of time-dependent phenomena. AIAA J. 7, 1170-1173 (1969)
    • (1969) AIAA J. , vol.7 , pp. 1170-1173
    • Fried, I.1
  • 19
    • 0014537398 scopus 로고
    • A general theory of finite elements ii. applications
    • Oden, J.T.: A general theory of finite elements ii. applications. Int. J. Numer. Methods Eng. 1, 247-259 (1969)
    • (1969) Int. J. Numer. Methods Eng. , vol.1 , pp. 247-259
    • Oden, J.T.1
  • 20
    • 0023960856 scopus 로고
    • Space-time finite element methods for elastodynamics: Formulations and error estimates
    • Hughes, T.J.R., Hulbert, G.M.: Space-time finite element methods for elastodynamics: Formulations and error estimates. Comput. Methods Appl. Mech. Eng. 66, 339-363 (1988)
    • (1988) Comput. Methods Appl. Mech. Eng. , vol.66 , pp. 339-363
    • Hughes, T.J.R.1    Hulbert, G.M.2
  • 21
    • 0003405947 scopus 로고
    • Space-time finite element methods for second order hyperbolic equations
    • PhD thesis, Department of Mechanical Engineering, Stanford University, Stanford
    • Hulbert, G.: Space-time finite element methods for second order hyperbolic equations. PhD thesis, Department of Mechanical Engineering, Stanford University, Stanford (1989)
    • (1989)
    • Hulbert, G.1
  • 22
    • 0026678731 scopus 로고
    • Time finite element methods for structural dynamics
    • Hulbert, G.M.: Time finite element methods for structural dynamics. Int. J. Numer. Methods Eng. 33, 307-331 (1992)
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 307-331
    • Hulbert, G.M.1
  • 23
    • 0025693468 scopus 로고
    • Space-time finite element methods for second-order hyperbolic equations
    • Hulbert, G.M., Hughes, T.J.R.: Space-time finite element methods for second-order hyperbolic equations. Comput. Methods Appl. Mech. Eng. 84, 327-348 (1990)
    • (1990) Comput. Methods Appl. Mech. Eng. , vol.84 , pp. 327-348
    • Hulbert, G.M.1    Hughes, T.J.R.2
  • 24
    • 33748251663 scopus 로고    scopus 로고
    • A time-discontinuous Galerkin method for the dynamical analysis of porous media
    • Chen, Z., Steeb, H., Diebels, S.: A time-discontinuous Galerkin method for the dynamical analysis of porous media. Int. J. Numer. Anal. Methods Geomech. 30, 1113-1134 (2006)
    • (2006) Int. J. Numer. Anal. Methods Geomech. , vol.30 , pp. 1113-1134
    • Chen, Z.1    Steeb, H.2    Diebels, S.3
  • 25
    • 0003781322 scopus 로고    scopus 로고
    • An hp -adaptive discontinuous finite element method for computational fluid dynamics
    • PhD thesis, The University of Texas at Austin
    • Baumann, C.E.: An hp -adaptive discontinuous finite element method for computational fluid dynamics. PhD thesis, The University of Texas at Austin (1997)
    • (1997)
    • Baumann, C.E.1
  • 27
    • 23044527716 scopus 로고    scopus 로고
    • Neglect of the fluid-extra stresses in volumetrically coupled solid-fluid problems
    • Diebels, S., Ehlers, W., Markert, B.: Neglect of the fluid-extra stresses in volumetrically coupled solid-fluid problems. Z. Angew. Math. Mech. 81, S521-S522 (2001)
    • (2001) Z. Angew. Math. Mech. , vol.81
    • Diebels, S.1    Ehlers, W.2    Markert, B.3
  • 28
    • 0142036606 scopus 로고    scopus 로고
    • Foundations of multiphasic and porous materials
    • In: Ehlers, W., Bluhm, J. (eds.) Springer, Berlin
    • Ehlers, W.: Foundations of multiphasic and porous materials. In: Ehlers, W., Bluhm, J. (eds.) Porous Media: Theory, Experiments and Numerical Applications, pp. 3-86. Springer, Berlin (2002)
    • (2002) Porous Media: Theory, Experiments and Numerical Applications , pp. 3-86
    • Ehlers, W.1
  • 29
    • 0345062335 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for convection-diffusion problems
    • Baumann, C.E., Oden, J.T.: A discontinuous hp finite element method for convection-diffusion problems. Comput Methods Appl. Mech. Eng. 175, 311-341 (1999)
    • (1999) Comput Methods Appl. Mech. Eng. , vol.175 , pp. 311-341
    • Baumann, C.E.1    Oden, J.T.2
  • 30
    • 85174221297 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods
    • Cockburn, B.: Discontinuous Galerkin methods. Z. Angew. Math. Mech. 11, 731-754 (2003)
    • (2003) Z. Angew. Math. Mech. , vol.11 , pp. 731-754
    • Cockburn, B.1
  • 31
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • Oden, J.T., Babuška, I., Baumann, C.E.: A discontinuous hp finite element method for diffusion problems. J. Comput. Phys. 146, 491-519 (1998)
    • (1998) J. Comput. Phys. , vol.146 , pp. 491-519
    • Oden, J.T.1    Babuška, I.2    Baumann, C.E.3
  • 34
    • 0042824223 scopus 로고    scopus 로고
    • Superconvergence and h (div) -projectin for discontinuous Galerkin methods
    • Bastian, P., Rivière, B.: Superconvergence and h (div) -projectin for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 42, 1043-1057 (2003)
    • (2003) Int. J. Numer. Methods Fluids , vol.42 , pp. 1043-1057
    • Bastian, P.1    Rivière, B.2
  • 35
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V
    • Cockburn, B., Shu, C.W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V. J. Chem. Phys. 141, 199-224 (1998)
    • (1998) J. Chem. Phys. , vol.141 , pp. 199-224
    • Cockburn, B.1    Shu, C.W.2
  • 36
    • 10644264359 scopus 로고    scopus 로고
    • New two-dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes
    • Hoteit, H., Ackerer, P., Mosé, R., Erhel, J., Philippe, B.: New two-dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes. Int. J. Numer. Methods Eng. 61, 2566-2593 (2004)
    • (2004) Int. J. Numer. Methods Eng. , vol.61 , pp. 2566-2593
    • Hoteit, H.1    Ackerer, P.2    Mosé, R.3    Erhel, J.4    Philippe, B.5
  • 38
    • 0023242924 scopus 로고
    • Viscous fingering in porous media
    • Homsy, G.M.: Viscous fingering in porous media. Ann. Rev. Fluid Mech. 19, 271-311 (1987)
    • (1987) Ann. Rev. Fluid Mech. , vol.19 , pp. 271-311
    • Homsy, G.M.1
  • 40
    • 0034628097 scopus 로고    scopus 로고
    • An adaptive-order discontinuous Galerkin method for the solution of the Euler equations of gas dynamics
    • Baumann, C.E., Oden, J.T.: An adaptive-order discontinuous Galerkin method for the solution of the Euler equations of gas dynamics. Int. J. Numer. Methods Eng. 47 (1-3), 61-73 (2000)
    • (2000) Int. J. Numer. Methods Eng. , vol.47 , Issue.1-3 , pp. 61-73
    • Baumann, C.E.1    Oden, J.T.2


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