메뉴 건너뛰기




Volumn 202, Issue 1, 2005, Pages 94-133

Variational multiscale stabilized FEM formulations for transport equations: Stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations

Author keywords

Karhunen Lo ve expansion; Monte Carlo; Polynomial chaos; Spectral stochastic FEM; Stochastic advection; Stochastic fluid flow; Subgrid scale models; Variational multiscale

Indexed keywords

DIFFUSION IN LIQUIDS; FINITE ELEMENT METHOD; MONTE CARLO METHODS; NAVIER STOKES EQUATIONS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; VISCOUS FLOW;

EID: 8744246329     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.06.019     Document Type: Article
Times cited : (45)

References (52)
  • 1
    • 0028667825 scopus 로고
    • Transport in three-dimensionally heterogenous aquifers: 1. dymanics of concentration fluctuations
    • V. Kapoor L. Gelhar Transport in three-dimensionally heterogenous aquifers: 1. dymanics of concentration fluctuations Water Resour. Res. 30 6 1994 1857-1864
    • (1994) Water Resour. Res. , vol.30 , Issue.6 , pp. 1857-1864
    • Kapoor, V.1    Gelhar, L.2
  • 2
    • 0028176315 scopus 로고
    • Nonreactive and reactive solute transport in three-dimensional heterogenous porous media: Mean displacement, plume spreading and uncertainty
    • D.T. Burr E.A. Sudicky R.L. Naff Nonreactive and reactive solute transport in three-dimensional heterogenous porous media: Mean displacement, plume spreading and uncertainty Water Resour. Res. 30 3 1994 791-815
    • (1994) Water Resour. Res. , vol.30 , Issue.3 , pp. 791-815
    • Burr, D.T.1    Sudicky, E.A.2    Naff, R.L.3
  • 3
    • 0025199514 scopus 로고
    • Modeling of ground-water contamination caused by organic solvent vapors
    • C. Mendoza T. McAlary Modeling of ground-water contamination caused by organic solvent vapors Ground Water 28 2 1990 199-206
    • (1990) Ground Water , vol.28 , Issue.2 , pp. 199-206
    • Mendoza, C.1    McAlary, T.2
  • 4
    • 0035424496 scopus 로고    scopus 로고
    • Parametric uncertainty analysis for thermal fluid calculations
    • J. Borggaard D. Pelletier E. Turgeon Parametric uncertainty analysis for thermal fluid calculations Nonlin. Anal. 47 2001 4533-4543
    • (2001) Nonlin. Anal. , vol.47 , pp. 4533-4543
    • Borggaard, J.1    Pelletier, D.2    Turgeon, E.3
  • 7
    • 84894429266 scopus 로고    scopus 로고
    • Sensitivity equations for turbulent flows
    • Proceedings of the 39th AIAA Aerospace Sciences Meeting and Exhibit, 2001-1060 AIAA Paper
    • A. Godfrey, E. Cliff, Sensitivity equations for turbulent flows, in: Proceedings of the 39th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2001-1060, 2001
    • (2001)
    • Godfrey, A.1    Cliff, E.2
  • 9
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier Hermite functionals
    • R.H. Cameron W.T. Martin The orthogonal development of nonlinear functionals in series of Fourier Hermite functionals Annal. Math. 48 1947 385-392
    • (1947) Annal. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 10
    • 0035506770 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow I. Basic formulation
    • O.P. Le Maitre O.M. Kino H.N. Najm R. Ghanem A stochastic projection method for fluid flow I. Basic formulation Comput. Phys. 173 2001 481-511
    • (2001) Comput. Phys. , vol.173 , pp. 481-511
    • Le Maitre, O.P.1    Kino, O.M.2    Najm, H.N.3    Ghanem, R.4
  • 12
    • 85189852110 scopus 로고    scopus 로고
    • A stochastic projection method for microchannel flow, Modeling and simulation of microsystems
    • Available from: www.cr.org , ISBN 0-9708275-0-4
    • O.P. Le Maitre, O.M. Knio, R. Ghanem, H.N. Najm, A stochastic projection method for microchannel flow, Modeling and simulation of microsystems. Available from: Www.cr.org , ISBN 0-9708275-0-4, 2001
    • (2001)
    • Le Maitre, O.P.1    Knio, O.M.2    Ghanem, R.3    Najm, H.N.4
  • 13
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogenous media
    • R. Ghanem Probabilistic characterization of transport in heterogenous media Comput. Meth. Appl. Mech. Eng. 158 1998 199-220
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.158 , pp. 199-220
    • Ghanem, R.1
  • 14
    • 0011074291 scopus 로고    scopus 로고
    • Stochastic modeling of flow-structure interactions using generalized polynomial chaos
    • D. Xiu D. Lucor C.-H. Su G.E. Karniadakis Stochastic modeling of flow-structure interactions using generalized polynomial chaos J. Fluids Eng. 125 2001 51-59
    • (2001) J. Fluids Eng. , vol.125 , pp. 51-59
    • Xiu, D.1    Lucor, D.2    Su, C.-H.3    Karniadakis, G.E.4
  • 15
    • 1142296114 scopus 로고    scopus 로고
    • Spectral polynomial chaos solutions of the stochastic advection equation
    • M. Jardak C.-H. Su G.E. Karniadakis Spectral polynomial chaos solutions of the stochastic advection equation J. Sci. Comput. 17 2002 319-338
    • (2002) J. Sci. Comput. , vol.17 , pp. 319-338
    • Jardak, M.1    Su, C.-H.2    Karniadakis, G.E.3
  • 16
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • D. Xiu G.E. Karniadakis Modeling uncertainty in flow simulations via generalized polynomial chaos J. Comput. Phys. 187 2003 137-167
    • (2003) J. Comput. Phys. , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.E.2
  • 17
    • 0013724411 scopus 로고
    • A multi-dimensional upwind scheme with no crosswind diffusion
    • T.J.R. Hughes (Ed.) ASME New York
    • T.J.R. Hughes A.N. Brooks A multi-dimensional upwind scheme with no crosswind diffusion In: T.J.R. Hughes (Ed.) Finite Element Methods for Convection Dominated Flows vol. 34 1979 ASME New York 19-35
    • (1979) Finite Element Methods for Convection Dominated Flows , vol.34 , pp. 19-35
    • Hughes, T.J.R.1    Brooks, A.N.2
  • 18
    • 0019607241 scopus 로고
    • Streamline-upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A.N. Brooks T.J.R. Hughes Streamline-upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 32 1982 199-259
    • (1982) Comput. Meth. Appl. Mech. Eng. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 19
    • 85138110008 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VII. The Galerkin least squares method for advective-diffusive equations
    • T.J.R. Hughes L.P. Franca G.M. Hulbert A new finite element formulation for computational fluid dynamics: VII. The Galerkin least squares method for advective-diffusive equations Comput. Meth. Appl. Mech. Eng. 59 1986 85-99
    • (1986) Comput. Meth. Appl. Mech. Eng. , vol.59 , pp. 85-99
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.M.3
  • 20
    • 0008476684 scopus 로고
    • Incompressible flow using stabilized bilinear and linear equal-order-interpolation velocity-pressure elements
    • Research Report UMSI 90/165 University of Minnesota Supercomputer Institute, Minneapolis
    • T.E. Tezduyar, R. Shih, S. Mittal, S.E. Ray, Incompressible flow using stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Research Report UMSI 90/165, University of Minnesota Supercomputer Institute, Minneapolis, 1990
    • (1990)
    • Tezduyar, T.E.1    Shih, R.2    Mittal, S.3    Ray, S.E.4
  • 21
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origin of stabilized methods
    • T.J.R. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origin of stabilized methods Comput. Meth. Appl. Mech. Eng. 127 1995 387-401
    • (1995) Comput. Meth. Appl. Mech. Eng. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 22
    • 0034234142 scopus 로고    scopus 로고
    • On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems
    • F. Ilinca J.-F. Hétu D. Pelletier On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems Comput. Meth. Appl. Mech. Eng. 188 2000 235-255
    • (2000) Comput. Meth. Appl. Mech. Eng. , vol.188 , pp. 235-255
    • Ilinca, F.1    Hétu, J.-F.2    Pelletier, D.3
  • 24
    • 0033264647 scopus 로고    scopus 로고
    • Stabilization of Galerkin approximations of transport equations by subgrid modeling
    • J.-L. Guermond Stabilization of Galerkin approximations of transport equations by subgrid modeling M2AN 33 1999 1293-1316
    • (1999) M2AN , vol.33 , pp. 1293-1316
    • Guermond, J.-L.1
  • 25
    • 0035955565 scopus 로고    scopus 로고
    • Variational subgrid scale formulations for the advection-diffusion-reaction equation
    • G. Haukeand A. Garcia-Olivares Variational subgrid scale formulations for the advection-diffusion-reaction equation Comput. Meth. Appl. Mech. Eng. 190 2001 6847-6865
    • (2001) Comput. Meth. Appl. Mech. Eng. , vol.190 , pp. 6847-6865
    • Haukeand, G.1    Garcia-Olivares, A.2
  • 26
    • 33748886945 scopus 로고    scopus 로고
    • Multiscale numerical methods for singularly-perturbed convection diffusion equations
    • P. Park T.Y. Hou Multiscale numerical methods for singularly-perturbed convection diffusion equations Intl. J. Comp. Meth. 1 1 2004 1-49
    • (2004) Intl. J. Comp. Meth. , vol.1 , Issue.1 , pp. 1-49
    • Park, P.1    Hou, T.Y.2
  • 27
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • T.Y. Hou X.H. Wu 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
  • 28
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method with rapidly oscillating coefficients
    • T.Y. Hou X.H. Wu Z.Q. Cai Convergence of a multiscale finite element method with rapidly oscillating coefficients Math. Comp. 68 1999 913-943
    • (1999) Math. Comp. , vol.68 , pp. 913-943
    • Hou, T.Y.1    Wu, X.H.2    Cai, Z.Q.3
  • 29
    • 0001769879 scopus 로고    scopus 로고
    • Large eddy simulation and the variational multiscale method
    • T.J.R. Hughes L. Mazzei K.E. Jansen Large eddy simulation and the variational multiscale method Comput. Visual. Sci. 3 2000 47-59
    • (2000) Comput. Visual. Sci. , vol.3 , pp. 47-59
    • Hughes, T.J.R.1    Mazzei, L.2    Jansen, K.E.3
  • 30
    • 0035367170 scopus 로고    scopus 로고
    • Large eddy simulation of turbulent channel flows by the variatioanl multiscale method
    • T.J.R. Hughes A.A. Oberai L. Mazzei Large eddy simulation of turbulent channel flows by the variatioanl multiscale method Phys. Fluid 13 2001 1784-1799
    • (2001) Phys. Fluid , vol.13 , pp. 1784-1799
    • Hughes, T.J.R.1    Oberai, A.A.2    Mazzei, L.3
  • 31
    • 0035065963 scopus 로고    scopus 로고
    • The multiscale formulation of large eddy simulation: Decay of isotropic turbulence
    • T.J.R. Hughes L. Mazzei A.A. Oberai A. Wray The multiscale formulation of large eddy simulation: Decay of isotropic turbulence Phys. Fluid 13 2001 505-512
    • (2001) Phys. Fluid , vol.13 , pp. 505-512
    • Hughes, T.J.R.1    Mazzei, L.2    Oberai, A.A.3    Wray, A.4
  • 32
    • 0003981320 scopus 로고
    • fourth ed. Berlin: Springer-Verlag
    • M. Loève Probability Theory fourth ed. 1977 Springer-Verlag Berlin
    • (1977) Probability Theory
    • Loève, M.1
  • 34
    • 0000786435 scopus 로고
    • The homogenous chaos
    • N. Wiener The homogenous chaos Am. J. Math. 60 1938 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 35
    • 0004013439 scopus 로고    scopus 로고
    • Stochastic processes and orthogonal polynomials
    • New York: Springer-Verlag
    • W. Schoutens Stochastic processes and orthogonal polynomials Lecture Notes in Statistics vol. 146 2000 Springer-Verlag New York
    • (2000) Lecture Notes in Statistics , vol.146
    • Schoutens, W.1
  • 36
    • 85189846981 scopus 로고    scopus 로고
    • On the well-posedness of generalized polynomial chaos expansions for the stochastic diffusion equation
    • (submitted)
    • D. Xiu, G.E. Karniadakis, On the well-posedness of generalized polynomial chaos expansions for the stochastic diffusion equation, SIAM J. Numer. Anal. (submitted)
    • SIAM J. Numer. Anal.
    • Xiu, D.1    Karniadakis, G.E.2
  • 37
    • 0037200448 scopus 로고    scopus 로고
    • Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
    • R. Codina Stabilized finite element approximation of transient incompressible flows using orthogonal subscales Comput. Meth. Appl. Mech. Eng. 191 39-40 2002 4295-4321
    • (2002) Comput. Meth. Appl. Mech. Eng. , vol.191 , Issue.39-40 , pp. 4295-4321
    • Codina, R.1
  • 38
    • 1142294211 scopus 로고    scopus 로고
    • Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using orthogonal subscales
    • R. Codina Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using orthogonal subscales Comput. Visual. Sci. 4 3 2002 167-174
    • (2002) Comput. Visual. Sci. , vol.4 , Issue.3 , pp. 167-174
    • Codina, R.1
  • 39
    • 8744242447 scopus 로고    scopus 로고
    • Multiscale-stabilized finite element method for miscible and immiscible flow in porous media
    • R. James T.W. Patzek Multiscale-stabilized finite element method for miscible and immiscible flow in porous media J. Hydraul. Res. 42 2004 131-140
    • (2004) J. Hydraul. Res. , vol.42 , pp. 131-140
    • James, R.1    Patzek, T.W.2
  • 40
    • 8744285949 scopus 로고    scopus 로고
    • The DG/VMS Method for unified turbulence simulation
    • AIAA Paper No. 2002-3124, MEMS Preprint No. 2002-029
    • S.S. Collis, The DG/VMS Method for unified turbulence simulation, AIAA Paper No. 2002-3124, MEMS Preprint No. 2002-029, 2002
    • (2002)
    • Collis, S.S.1
  • 41
    • 85085401629 scopus 로고    scopus 로고
    • Variational multiscale modeling for turbulence control
    • AIAA Paper No. 2002-3280, MEMS Preprint No. 2002-024
    • S. Ramakrishnan, S.S. Collis, Variational multiscale modeling for turbulence control, AIAA Paper No. 2002-3280, MEMS Preprint No. 2002-024, 2002
    • (2002)
    • Ramakrishnan, S.1    Collis, S.S.2
  • 42
    • 0035368136 scopus 로고    scopus 로고
    • Monitoring unresolved scales in multiscale turbulence modeling
    • S.S. Collis Monitoring unresolved scales in multiscale turbulence modeling Phys. Fluid 13 6 2001 1800-1806
    • (2001) Phys. Fluid , vol.13 , Issue.6 , pp. 1800-1806
    • Collis, S.S.1
  • 43
    • 0030158797 scopus 로고    scopus 로고
    • Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations
    • A. Russo Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 132 1996 335-343
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.132 , pp. 335-343
    • Russo, A.1
  • 44
    • 0027611385 scopus 로고
    • Convergence analysis of Galerkin least-squares methods for advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations
    • L.P. Franca T.J.R. Hughes Convergence analysis of Galerkin least-squares methods for advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 105 1993 285-298
    • (1993) Comput. Meth. Appl. Mech. Eng. , vol.105 , pp. 285-298
    • Franca, L.P.1    Hughes, T.J.R.2
  • 46
    • 0028372424 scopus 로고
    • Finite element solution strategies for large-scale flow simulations
    • T.E. Tezduyar M. Behr Finite element solution strategies for large-scale flow simulations Comput. Meth. Appl. Mech. Eng. 112 1994 3-24
    • (1994) Comput. Meth. Appl. Mech. Eng. , vol.112 , pp. 3-24
    • Tezduyar, T.E.1    Behr, M.2
  • 47
    • 0032473210 scopus 로고    scopus 로고
    • Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations
    • N. Nigro M. Storti S. Idelsohn T.E. Tezduyar Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 154 1998 203-228
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.154 , pp. 203-228
    • Nigro, N.1    Storti, M.2    Idelsohn, S.3    Tezduyar, T.E.4
  • 48
    • 0037143620 scopus 로고    scopus 로고
    • On streamline diffusion arising in Galerkin FEM with predictor/multi-corrector time integration
    • Y. Eguchi On streamline diffusion arising in Galerkin FEM with predictor/multi-corrector time integration Int. J. Num. Meth. Eng. 39 2002 1037-1052
    • (2002) Int. J. Num. Meth. Eng. , vol.39 , pp. 1037-1052
    • Eguchi, Y.1
  • 49
    • 49049143188 scopus 로고
    • High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
    • U. Ghia K.N. Ghia C.T. Shin High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method J. Comput. Phys. 48 1982 387-411
    • (1982) J. Comput. Phys. , vol.48 , pp. 387-411
    • Ghia, U.1    Ghia, K.N.2    Shin, C.T.3
  • 50
    • 84912932876 scopus 로고
    • Analytical and numerical studies of the structure of steady separated flows
    • O.R. Burggraf Analytical and numerical studies of the structure of steady separated flows J. Fluid. Mech. 24 1966 113-151
    • (1966) J. Fluid. Mech. , vol.24 , pp. 113-151
    • Burggraf, O.R.1
  • 51
    • 84959704290 scopus 로고
    • Steady flows in rectangular cavities
    • F. Pan A. Acrivos Steady flows in rectangular cavities J. Fluid. Mech. 28 1967 643-655
    • (1967) J. Fluid. Mech. , vol.28 , pp. 643-655
    • Pan, F.1    Acrivos, A.2
  • 52
    • 0015810099 scopus 로고
    • Numerical study of viscous flow in a cavity
    • J.D. Bozeman C. Dalton Numerical study of viscous flow in a cavity J. Comput. Phys. 12 1973 348-363
    • (1973) J. Comput. Phys. , vol.12 , pp. 348-363
    • Bozeman, J.D.1    Dalton, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.