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Volumn 43, Issue 4, 2005, Pages 1572-1595

A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations

Author keywords

Discontinuous Galerkin; Error analysis; Fully discrete scheme; High order method; Navier Stokes

Indexed keywords

DISCONTINUOUS GALERKIN; FULLY DISCRETE SCHEME; HIGH ORDER METHOD;

EID: 30344470638     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903434862     Document Type: Article
Times cited : (42)

References (31)
  • 1
  • 5
    • 0001757540 scopus 로고
    • Théorie de l'écoulement tourbillant
    • J. BOUSSINESQ, Théorie de l'écoulement tourbillant, Mem. Pres. Acad. Sci. Paris, 23 (1877), pp. 46-50.
    • (1877) Mem. Pres. Acad. Sci. Paris , vol.23 , pp. 46-50
    • Boussinesq, J.1
  • 7
    • 84966199862 scopus 로고
    • Nonconforming finite elements for the Stokes problem
    • M. CROUZEIX AND R. FALK, Nonconforming finite elements for the Stokes problem, Math. Comp., 52 (1989), pp. 437-456.
    • (1989) Math. Comp. , vol.52 , pp. 437-456
    • Crouzeix, M.1    Falk, R.2
  • 8
    • 0015762231 scopus 로고
    • Conforming and nonconforming finite element methods for solving the stationary Stokes equations
    • M. CROUZEIX AND P. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations, RAIRO Ser. Rouge, (1973), pp. 33-75.
    • (1973) RAIRO Ser. Rouge , pp. 33-75
    • Crouzeix, M.1    Raviart, P.2
  • 9
    • 0020735864 scopus 로고
    • A non-conforming piecewise quadratic finite element on triangles
    • M. FORTIN AND M. SOULIE, A non-conforming piecewise quadratic finite element on triangles, Internat. J. Numer. Methods, 19 (1983), pp. 505-520.
    • (1983) Internat. J. Numer. Methods , vol.19 , pp. 505-520
    • Fortin, M.1    Soulie, M.2
  • 10
    • 5244265345 scopus 로고
    • Turbulence: Challenges for theory and experiment
    • U. FRISCH AND S. A. ORSZAG, Turbulence: Challenges for theory and experiment, Phys. Today, (1990), pp. 24-32.
    • (1990) Phys. Today , pp. 24-32
    • Frisch, U.1    Orszag, S.A.2
  • 11
    • 0003197516 scopus 로고
    • Finite element approximation of the Navier-stokes equations
    • Springer-Verlag, Berlin
    • V. GIRAULT AND P.-A. RAVIART, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Math. 749, Springer-Verlag, Berlin, 1979.
    • (1979) Lecture Notes in Math. , vol.749
    • Girault, V.1    Raviart, P.-A.2
  • 12
    • 11244280117 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-stokes problems
    • V. GIRAULT, B. RIVIÈRE, AND M. F. WHEELER, A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems, Math. Comp., 74 (2005), pp. 53-84.
    • (2005) Math. Comp. , vol.74 , pp. 53-84
    • Girault, V.1    Rivière, B.2    Wheeler, M.F.3
  • 13
    • 0037595549 scopus 로고    scopus 로고
    • A quasi-local interpolation operator preserving the discrete divergence
    • V. GIRAULT AND R. SCOTT, A quasi-local interpolation operator preserving the discrete divergence, Calcolo, 40 (2003), pp. 1-19.
    • (2003) Calcolo , vol.40 , pp. 1-19
    • Girault, V.1    Scott, R.2
  • 14
    • 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 Math. Model. Numer. Anal., 33 (1999), pp. 1293-1316.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , pp. 1293-1316
    • Guermond, J.-L.1
  • 15
    • 0025416424 scopus 로고
    • Finite-element approximation of the nonstationary Navier-stokes problem part IV: Error analysis for second-order time discretization
    • J. G. HEYWOOD AND R. RANNACHER, Finite-element approximation of the nonstationary Navier-Stokes problem part IV: Error analysis for second-order time discretization, SIAM J. Numer. Anal., 27 (1990), pp. 353-384.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 353-384
    • Heywood, J.G.1    Rannacher, R.2
  • 16
    • 0029405472 scopus 로고
    • The multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods
    • T. J. R. HUGHES, The multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods, Comput. Methods Appl. Mech. Engrg., 127 (1995), pp. 387-401.
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 17
    • 0001769879 scopus 로고    scopus 로고
    • Large eddy simulation and the variational multiscale method
    • T. J. R. HUGHES, L. MAZZEI, AND K. E. JANSEN, Large eddy simulation and the variational multiscale method, Comput. Visual. Sci., 3 (2000), pp. 47-59.
    • (2000) Comput. Visual. Sci. , vol.3 , pp. 47-59
    • Hughes, T.J.R.1    Mazzei, L.2    Jansen, K.E.3
  • 18
    • 0035367170 scopus 로고    scopus 로고
    • Large eddy simulation of turbulent channel flows by the variational multiscale method
    • T. J. R. HUGHES, A. A. OBERAI, AND L. MAZZEI, Large eddy simulation of turbulent channel flows by the variational multiscale method, Phys. Fluids, 13 (2001), pp. 1784-1799.
    • (2001) Phys. Fluids , vol.13 , pp. 1784-1799
    • Hughes, T.J.R.1    Oberai, A.A.2    Mazzei, L.3
  • 19
    • 0000650648 scopus 로고    scopus 로고
    • Approximating the larger eddies in fluid motion. III. The Boussinesq model for turbulent fluctuations
    • T. ILIESCU AND W. J. LAYTON, Approximating the larger eddies in fluid motion. III. The Boussinesq model for turbulent fluctuations, An. Stunt. Univ. Al. I. Cuza las., Mat. (N.S.), 44 (1998), pp. 245-261.
    • (1998) An. Stunt. Univ. Al. I. Cuza Las., Mat. (N.S.) , vol.44 , pp. 245-261
    • Iliescu, T.1    Layton, W.J.2
  • 20
    • 25444505626 scopus 로고    scopus 로고
    • A finite element variational multiscale method for the Navier-stokes equations
    • V. JOHN AND S. KAYA, A finite element variational multiscale method for the Navier-Stokes equations, SIAM J. Sci. Comput., 26 (2005), pp. 1485-1503.
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 1485-1503
    • John, V.1    Kaya, S.2
  • 21
    • 0001408252 scopus 로고    scopus 로고
    • Nonconforming finite element method for the stationary Navier-stokes equations
    • O. A. KARAKASHIAN AND W. N. JUREIDINI, Nonconforming finite element method for the stationary Navier-Stokes equations, SIAM J. Numer. Anal., 35 (1998), pp. 93-120.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 93-120
    • Karakashian, O.A.1    Jureidini, W.N.2
  • 22
    • 22144494500 scopus 로고    scopus 로고
    • Subgrid-scale eddy viscosity methods are variational multiscale methods
    • University of Pittsburgh, Pittsburgh, PA
    • S. KAYA AND W. LAYTON, Subgrid-scale eddy viscosity methods are variational multiscale methods, Tech. report TR-MATH 03-05, University of Pittsburgh, Pittsburgh, PA, 2003.
    • (2003) Tech. Report , vol.TR-MATH 03-05
    • Kaya, S.1    Layton, W.2
  • 23
    • 84858939042 scopus 로고    scopus 로고
    • Analysis of a discontinuous Galerkin and eddy viscosity method for Navier-Stokes
    • University of Pittsburgh, Pittsburgh, PA
    • S. KAYA AND B. RIVIÈRE, Analysis of a discontinuous Galerkin and eddy viscosity method for Navier-Stokes, Tech. report TR-MATH 03-14, University of Pittsburgh, Pittsburgh, PA, 2003.
    • (2003) Tech. Report , vol.TR-MATH 03-14
    • Kaya, S.1    Rivière, B.2
  • 24
    • 0037175406 scopus 로고    scopus 로고
    • A connection between subgrid scale eddy viscosity and mixed methods
    • W. J. LAYTON, A connection between subgrid scale eddy viscosity and mixed methods, Appl. Math. Comput., 133 (2002), pp. 147-157.
    • (2002) Appl. Math. Comput. , vol.133 , pp. 147-157
    • Layton, W.J.1
  • 27
    • 0000961081 scopus 로고
    • Analysis of spectral vanishing viscosity method for periodic conservation laws
    • Y. MADAY AND E. TADMOR, Analysis of spectral vanishing viscosity method for periodic conservation laws, SIAM J. Numer. Anal., 26 (1989), pp. 854-870.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 854-870
    • Maday, Y.1    Tadmor, E.2
  • 28
    • 0003630916 scopus 로고
    • Triangular mesh methods for the neutron transport equation
    • Los Alamos Scientific Laboratory, Los Alamos, NM
    • W. H. REED AND T. R. HILL, Triangular mesh methods for the neutron transport equation, Tech. report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM, 1973.
    • (1973) Tech. Report , vol.LA-UR-73-479
    • Reed, W.H.1    Hill, T.R.2
  • 29
    • 0001957739 scopus 로고
    • General circulation experiments with the primitive equation, I: The basic experiment
    • J. SMAGORINSKY, General circulation experiments with the primitive equation, I: The basic experiment, Month. Weath. Rev., 91 (1963), pp. 99-164.
    • (1963) Month. Weath. Rev. , vol.91 , pp. 99-164
    • Smagorinsky, J.1
  • 30
    • 0000372952 scopus 로고
    • Navier-stokes Equations and Nonlinear Functional Analysis
    • 2nd ed., SIAM, Philadelphia
    • R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conf. Ser. in Appl. Math. 66, 2nd ed., SIAM, Philadelphia, 1995.
    • (1995) CBMS-NSF Regional Conf. Ser. in Appl. Math. , vol.66
    • Temam, R.1
  • 31
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • M. F. WHEELER, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal., 15 (1978), pp. 152-161.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.