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Volumn 229, Issue 10, 2010, Pages 3957-3969

An exponential integrator for advection-dominated reactive transport in heterogeneous porous media

Author keywords

Advection diffusion equation; Exponential integration; Fast time integrators; Krylov subspace; L ja points; Porous media

Indexed keywords

ADVECTION; GEOLOGY; LINEAR SYSTEMS; NUMERICAL METHODS;

EID: 78649442789     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.01.037     Document Type: Article
Times cited : (39)

References (43)
  • 1
    • 2942612789 scopus 로고    scopus 로고
    • Tenth SPE comparative solution project: a comparison of upscaling techniques
    • M.A. Christie, M.J. Blunt, Tenth SPE comparative solution project: a comparison of upscaling techniques, SPE Reserv. Eval. Eng. 4 (4) (2001) 308-317.
    • (2001) SPE Reserv. Eval. Eng. , vol.4 , Issue.4 , pp. 308-317
    • Christie, M.A.1    Blunt, M.J.2
  • 2
    • 3042778578 scopus 로고    scopus 로고
    • Fluid flow partitioning between fractures and a permeable rock matrix
    • doi:10.1029/2003GL019027
    • S.K. Matthäi, M. Belayneh, Fluid flow partitioning between fractures and a permeable rock matrix, Geophys. Res. Lett. 31 (7) (2004) L07602, doi:10.1029/2003GL019027.
    • (2004) Geophys. Res. Lett. , vol.31 , Issue.7
    • Matthäi, S.K.1    Belayneh, M.2
  • 3
    • 33845247896 scopus 로고    scopus 로고
    • Modeling non-Fickian transport in geological formations as a continuous time random walk
    • doi:10.1029/2005RG000178
    • B. Berkowitz, A. Cortis, M. Dentz, H. Scher, Modeling non-Fickian transport in geological formations as a continuous time random walk, Rev. Geophys. 44 (2) (2006) RG2003, doi:10.1029/2005RG000178.
    • (2006) Rev. Geophys. , vol.44 , Issue.2
    • Berkowitz, B.1    Cortis, A.2    Dentz, M.3    Scher, H.4
  • 4
    • 0034107154 scopus 로고    scopus 로고
    • Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments
    • O. Cirpka, P. Kitanidis, Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments, Water Resour. Res. 36 (5) (2000) 1221-1236.
    • (2000) Water Resour. Res. , vol.36 , Issue.5 , pp. 1221-1236
    • Cirpka, O.1    Kitanidis, P.2
  • 5
    • 49449097677 scopus 로고    scopus 로고
    • Mixing-induced precipitation: experimental study and multi-scale numerical analysis
    • doi:10.1029/2006WR005725
    • A.M. Tartakovsky, G. Redden, P.L. Lichtner, T.D. Scheibe, P. Meakin, Mixing-induced precipitation: experimental study and multi-scale numerical analysis, Water Resour. Res. 44 (6) (2008) W06S04, doi:10.1029/2006WR005725.
    • (2008) Water Resour. Res. , vol.44 , Issue.6
    • Tartakovsky, A.M.1    Redden, G.2    Lichtner, P.L.3    Scheibe, T.D.4    Meakin, P.5
  • 6
    • 70349886558 scopus 로고    scopus 로고
    • Effects of incomplete mixing on multicomponent reactive transport
    • A.M. Tartakovsky, G.D. Tartakovsky, T.D. Scheibe, Effects of incomplete mixing on multicomponent reactive transport, Adv. Water Resour. 31 (11) (2009) 1674-1679.
    • (2009) Adv. Water Resour. , vol.31 , Issue.11 , pp. 1674-1679
    • Tartakovsky, A.M.1    Tartakovsky, G.D.2    Scheibe, T.D.3
  • 7
    • 33746329299 scopus 로고    scopus 로고
    • Uncertainty quantification for porous media flows
    • M. Christie, V. Demyanov, D. Ebras, Uncertainty quantification for porous media flows, J. Comput. Phys. 217 (1) (2006) 143-158.
    • (2006) J. Comput. Phys. , vol.217 , Issue.1 , pp. 143-158
    • Christie, M.1    Demyanov, V.2    Ebras, D.3
  • 8
    • 0037336326 scopus 로고    scopus 로고
    • On balanced approximations for time integration of multiple time scale systems
    • D.A. Knoll, L. Chacon, L.G. Margolin, V.A. Mousseau, On balanced approximations for time integration of multiple time scale systems, J. Comput. Phys. 185 (2) (2003) 583-611.
    • (2003) J. Comput. Phys. , vol.185 , Issue.2 , pp. 583-611
    • Knoll, D.A.1    Chacon, L.2    Margolin, L.G.3    Mousseau, V.A.4
  • 9
    • 1442282996 scopus 로고    scopus 로고
    • Studies of the accuracy of time integration methods for reaction-diffusion equations
    • D.L. Ropp, J.N. Shadid, C.C. Ober, Studies of the accuracy of time integration methods for reaction-diffusion equations, J. Comput. Phys. 194 (2) (2004) 544-577.
    • (2004) J. Comput. Phys. , vol.194 , Issue.2 , pp. 544-577
    • Ropp, D.L.1    Shadid, J.N.2    Ober, C.C.3
  • 10
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (3) (1968) 506-517.
    • (1968) SIAM J. Numer. Anal. , vol.5 , Issue.3 , pp. 506-517
    • Strang, G.1
  • 11
    • 84977782256 scopus 로고    scopus 로고
    • Approaches to modeling of reactive transport in porous media
    • P.C. Lichtner, C.I. Steefel, E.H. Oelkers (Eds.), Mineralogical Society of America, Chantilly
    • C.I. Steefel, K.T.B. MacQuarrie, Approaches to modeling of reactive transport in porous media, in: P.C. Lichtner, C.I. Steefel, E.H. Oelkers (Eds.), Reviews in Mineralogy and Geochemistry, vol. 34, Mineralogical Society of America, Chantilly, 1996, pp. 83-129.
    • (1996) Reviews in Mineralogy and Geochemistry , vol.34 , pp. 83-129
    • Steefel, C.I.1    MacQuarrie, K.T.B.2
  • 12
    • 0001737039 scopus 로고
    • Implicit explicit methods for time dependent partial differential equations
    • U.M. Ascher, S.J. Ruuth, B.T.R. Wetton, Implicit explicit methods for time dependent partial differential equations, SIAM J. Numer. Anal. 32 (3) (1995) 797-823.
    • (1995) SIAM J. Numer. Anal. , vol.32 , Issue.3 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 14
    • 0030085448 scopus 로고    scopus 로고
    • Simulating flow in heterogeneous systems using streamtubes and streamlines
    • M.R. Thiele, R.P. Batycky, F. Orr, Simulating flow in heterogeneous systems using streamtubes and streamlines, SPE Reserv. Eng. 11 (1) (1996) 5-12.
    • (1996) SPE Reserv. Eng. , vol.11 , Issue.1 , pp. 5-12
    • Thiele, M.R.1    Batycky, R.P.2    Orr, F.3
  • 15
    • 2442639374 scopus 로고    scopus 로고
    • Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs
    • doi:101029/2003WR002772
    • G. DiDonato, M.J. Blunt, Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs, Water Resour. Res. 40 (4) (2004) W04203, doi:10.1029/2003WR002772.
    • (2004) Water Resour. Res. , vol.40 , Issue.4
    • DiDonato, G.1    Blunt, M.J.2
  • 16
    • 0031572117 scopus 로고    scopus 로고
    • Adaptive mesh refinement and multilevel iteration for flow in porous media
    • R.D. Hornung, J.A. Trangenstein, Adaptive mesh refinement and multilevel iteration for flow in porous media, J. Comput. Phys. 136 (2) (1997) 522-545.
    • (1997) J. Comput. Phys. , vol.136 , Issue.2 , pp. 522-545
    • Hornung, R.D.1    Trangenstein, J.A.2
  • 17
    • 17144413049 scopus 로고    scopus 로고
    • A new asynchronous methodology for modeling of physical systems: breaking the curse of courant condition
    • H. Karimabadi, J. Driscoll, Y.A. Omelchenko, N. Omidi, A new asynchronous methodology for modeling of physical systems: breaking the curse of courant condition, J. Comput. Phys. 205 (2) (2005) 755-775.
    • (2005) J. Comput. Phys. , vol.205 , Issue.2 , pp. 755-775
    • Karimabadi, H.1    Driscoll, J.2    Omelchenko, Y.A.3    Omidi, N.4
  • 18
    • 33646136667 scopus 로고    scopus 로고
    • Self-adaptive time integration of flux-conservative equations with sources
    • Y.A. Omelchenko, H. Karimabadi, Self-adaptive time integration of flux-conservative equations with sources, J. Comput. Phys. 216 (1) (2006) 179-194.
    • (2006) J. Comput. Phys. , vol.216 , Issue.1 , pp. 179-194
    • Omelchenko, Y.A.1    Karimabadi, H.2
  • 20
    • 22544474620 scopus 로고    scopus 로고
    • Fourth-order time stepping for stiff PDES
    • A.K. Kassam, L.N. Trefethen, Fourth-order time stepping for stiff PDES, SIAM J. Comput. 26 (4) (2005) 1214-1233.
    • (2005) SIAM J. Comput. , vol.26 , Issue.4 , pp. 1214-1233
    • Kassam, A.K.1    Trefethen, L.N.2
  • 22
    • 33746631920 scopus 로고    scopus 로고
    • The RELPM exponential integrator for FE discretizations of advection-diffusion equations
    • M. Bubak, G.D. Van Albada, P. Sloot (Eds.), Springer-Verlag, Berlin/Heidelberg
    • L. Bergamaschi, M. Caliari, M. Vianello, The RELPM exponential integrator for FE discretizations of advection-diffusion equations, in: M. Bubak, G.D. Van Albada, P. Sloot (Eds.), Lecture Notes in Computer Sciences, vol. 3039, Springer-Verlag, Berlin/Heidelberg, 2004, pp. 434-442.
    • (2004) Lecture Notes in Computer Sciences , vol.3039 , pp. 434-442
    • Bergamaschi, L.1    Caliari, M.2    Vianello, M.3
  • 23
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • M. Hochbruck, C. Lubich, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal. 34 (5) (1997) 1911-1925.
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 24
    • 0032010619 scopus 로고    scopus 로고
    • Expokit: a software package for computing matrix exponentials
    • R.B. Sidje, Expokit: a software package for computing matrix exponentials, ACM Trans. Math. Software 24 (1) (1998) 130-156.
    • (1998) ACM Trans. Math. Software , vol.24 , Issue.1 , pp. 130-156
    • Sidje, R.B.1
  • 25
    • 67349229829 scopus 로고    scopus 로고
    • A massively parallel exponential integrator for advection-diffusion models
    • A. Martinez, L. Bergamaschi, M. Caliari, M. Vianello, A massively parallel exponential integrator for advection-diffusion models, J. Comput. Appl. Math. 231 (1) (2009) 82-91.
    • (2009) J. Comput. Appl. Math. , vol.231 , Issue.1 , pp. 82-91
    • Martinez, A.1    Bergamaschi, L.2    Caliari, M.3    Vianello, M.4
  • 26
    • 33746647775 scopus 로고    scopus 로고
    • Comparing Léja and Krylov approximations of large scale matrix exponentials
    • L. Bergamaschi, M. Caliari, A. Martinez, M. Vianello, Comparing Léja and Krylov approximations of large scale matrix exponentials, Comput. Sci. - ICCS 3994 (2006) 685-692.
    • (2006) Comput. Sci. - ICCS , vol.3994 , pp. 685-692
    • Bergamaschi, L.1    Caliari, M.2    Martinez, A.3    Vianello, M.4
  • 27
    • 4444264388 scopus 로고    scopus 로고
    • Interpolating discrete advection diffusion propagators at Léja sequences
    • M. Caliari, M. Vianello, L. Bergamaschi, Interpolating discrete advection diffusion propagators at Léja sequences, J. Comput. Appl. Math. 172 (1) (2004) 79-99.
    • (2004) J. Comput. Appl. Math. , vol.172 , Issue.1 , pp. 79-99
    • Caliari, M.1    Vianello, M.2    Bergamaschi, L.3
  • 28
    • 34748841428 scopus 로고    scopus 로고
    • The LEM exponential integrator for advection-diffusion-reaction equations
    • M. Caliari, M. Vianello, L. Bergamaschi, The LEM exponential integrator for advection-diffusion-reaction equations, J. Comput. Appl. Math. 210 (1-2) (2007) 56-63.
    • (2007) J. Comput. Appl. Math. , vol.210 , Issue.1-2 , pp. 56-63
    • Caliari, M.1    Vianello, M.2    Bergamaschi, L.3
  • 29
    • 58249085985 scopus 로고    scopus 로고
    • Implementation of exponential Rosenbrock-type integrators
    • M. Caliari, A. Ostermann, Implementation of exponential Rosenbrock-type integrators, Appl. Numer. Math. 59 (3-4) (2009) 568-581.
    • (2009) Appl. Numer. Math. , vol.59 , Issue.3-4 , pp. 568-581
    • Caliari, M.1    Ostermann, A.2
  • 30
    • 70350322945 scopus 로고    scopus 로고
    • Finite volume methods
    • in: P.G. Ciarlet, J.L. Lions (Eds.), North-Holland, Amsterdam
    • R. Eymard, T. Gallouet, R. Herbin, Finite volume methods, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. 7, North-Holland, Amsterdam, 2000, pp. 713-1020.
    • (2000) Handbook of Numerical Analysis , vol.7 , pp. 713-1020
    • Eymard, R.1    Gallouet, T.2    Herbin, R.3
  • 32
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • S.M. Cox, P.C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys. 176 (2) (2002) 430-455.
    • (2002) J. Comput. Phys. , vol.176 , Issue.2 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 33
  • 35
    • 34547700082 scopus 로고    scopus 로고
    • Accurate evaluation of divided differences for polynomial interpolation of exponential propagators
    • M. Caliari, Accurate evaluation of divided differences for polynomial interpolation of exponential propagators, Computing 80 (2) (2007) 189-201.
    • (2007) Computing , vol.80 , Issue.2 , pp. 189-201
    • Caliari, M.1
  • 36
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • C. Moler, C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev. 45 (1) (2003) 3-49.
    • (2003) SIAM Rev , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 38
    • 0032633849 scopus 로고    scopus 로고
    • Analytical solution of a spatially variable coefficient advection-diffusion equation in up to three dimensions
    • C. Zoppou, J.H. Knight, Analytical solution of a spatially variable coefficient advection-diffusion equation in up to three dimensions, Appl. Math. Model. 23 (9) (1999) 667-685.
    • (1999) Appl. Math. Model. , vol.23 , Issue.9 , pp. 667-685
    • Zoppou, C.1    Knight, J.H.2
  • 40
    • 0035282142 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • K. Stüben, 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
  • 41
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • T. Hou, X. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys. 134 (1) (1997) 169-189.
    • (1997) J. Comput. Phys. , vol.134 , Issue.1 , pp. 169-189
    • Hou, T.1    Wu, X.2
  • 42
    • 0000713961 scopus 로고    scopus 로고
    • Convergence of a nonconformal multiscale finite element method
    • Y. Efendiev, T. Hou, X. Wu, Convergence of a nonconformal multiscale finite element method, SIAM J. Numer. Anal. 37 (3) (2000) 888-910.
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 888-910
    • Efendiev, Y.1    Hou, T.2    Wu, X.3
  • 43
    • 0037408094 scopus 로고    scopus 로고
    • Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
    • P. Jenny, H.A. Tchelepi, Multi-scale finite-volume method for elliptic problems in subsurface flow simulation, J. Comput. Phys. 187 (1) (2003) 47-67.
    • (2003) J. Comput. Phys. , vol.187 , Issue.1 , pp. 47-67
    • Jenny, P.1    Tchelepi, H.A.2


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