메뉴 건너뛰기




Volumn 47, Issue 1, 2008, Pages 250-270

A semi-implicit scheme for stationary statistical properties of the infinite Prandtl number model

Author keywords

Infinite Prandtl number model; Nusselt number; Stationary statistical property; Uniformly dissipativo scheme

Indexed keywords

COMPLEX SYSTEMS; DISSIPATIVITY; FINITE-TIME CONVERGENCE; INFINITE DIMENSIONAL; INFINITE PRANDTL NUMBER; INFINITE PRANDTL NUMBER MODEL; KEY CHARACTERISTICS; NUMERICAL SCHEME; SEMI-IMPLICIT; SEMI-IMPLICIT SCHEME; STATISTICAL PROPERTIES;

EID: 61349176737     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/080713501     Document Type: Article
Times cited : (13)

References (50)
  • 1
    • 31144435555 scopus 로고    scopus 로고
    • Turbulent thermal convection at large Rayleigh numbers for a Boussinesq fluid of constant Prandtl number
    • G. AMATI, K. KOAL, F. MASSAIOLI, K. R. SREENIVASAN, AND R. VERZIOOO, Turbulent thermal convection at large Rayleigh numbers for a Boussinesq fluid of constant Prandtl number, Physics of Fluids, 17 (2005), p. 121701.
    • (2005) Physics of Fluids , vol.17 , pp. 121701
    • Amati, G.1    Koal, K.2    Massaioli, F.3    Sreenivasan, K.R.4    Verziooo, R.5
  • 2
    • 0010738698 scopus 로고    scopus 로고
    • Ergodic theory and topological dynamics of group actions on homogeneous spaces
    • Cambridge University Press, Cambridge, UK
    • M.B. BEKKA AND M. MAYER, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, London Mathematical Society Lecture Note Series 269, Cambridge University Press, Cambridge, UK, 2000.
    • (2000) London Mathematical Society Lecture Note Series , vol.269
    • Bekka, M.B.1    Mayer, M.2
  • 4
    • 0034592313 scopus 로고    scopus 로고
    • Recent developments in Rayleigh-Bénard convection
    • Palo Alto, CA
    • E. BODENSOHATZ, W. PESOH, AND G. AHLERS, Recent developments in Rayleigh-Bénard convection, Annu. Rev. Fluid Moch. 32, Palo Alto, CA, 2000, pp. 709-778.
    • (2000) Annu. Rev. Fluid Moch. , vol.32 , pp. 709-778
    • Bodensohatz, E.1    Pesoh, W.2    Ahlers, G.3
  • 5
    • 33645025247 scopus 로고    scopus 로고
    • Exponentially growing solutions in homogeneous Rayleigh-Bénard convection
    • E. CALZAVARINI, C. R. DOERING, J. D. GIBBON, D. LOHSE, A. TANABE, AND F. TOSOHI, Exponentially growing solutions in homogeneous Rayleigh-Bénard convection, Phys. Rev. E. (3), 73 (2006), p. 035301.
    • (2006) Phys. Rev. E. , vol.73 , Issue.3 , pp. 035301
    • Calzavarini, E.1    Doering, C.R.2    Gibbon, J.D.3    Lohse, D.4    Tanabe, A.5    Tosohi, F.6
  • 7
    • 0013415879 scopus 로고    scopus 로고
    • Heat transfer in convective turbulence
    • P. CONSTANTIN AND C. R. DOERING, Heat transfer in convective turbulence, Nonlinoarity, 9 (1996), pp. 1049-1060.
    • (1996) Nonlinoarity , vol.9 , pp. 1049-1060
    • Constantin, P.1    Doering, C.R.2
  • 8
    • 0032589534 scopus 로고    scopus 로고
    • Infinite Prandtl number convection
    • P. CONSTANTIN AND C. R. DOERING, Infinite Prandtl number convection, J. Stat. Phys., 94 (1999), pp. 159-172.
    • (1999) J. Stat. Phys. , vol.94 , pp. 159-172
    • Constantin, P.1    Doering, C.R.2
  • 9
    • 34250706219 scopus 로고    scopus 로고
    • A discrete Kato-type theorem on inviscid limit of Navier-Stokes flows
    • W. CHENG AND X. WANG, A discrete Kato-type theorem on inviscid limit of Navier-Stokes flows, J. Math. Phys., 48 (2007), p. 065303.
    • (2007) J. Math. Phys. , vol.48 , pp. 065303
    • Cheng, W.1    Wang, X.2
  • 10
    • 77952684395 scopus 로고    scopus 로고
    • A uniformly dissipative scheme for stationary statistical properties of the infinite Prandtl number model for convection
    • W. CHENG AND X. WANG, A uniformly dissipative scheme for stationary statistical properties of the infinite Prandtl number model for convection, Appl. Math. Lett., in press.
    • Appl. Math. Lett., in Press
    • Cheng, W.1    Wang, X.2
  • 12
    • 33748268887 scopus 로고    scopus 로고
    • Bounds on vertical heat transport for infinite- Prandtl-number Rayleigh-Bénard convection
    • C. R. DOERING, F. OTTO, AND M. G. REZNIKOFF, Bounds on vertical heat transport for infinite- Prandtl-number Rayleigh-Bénard convection, J. Fluid Moch., 560 (2006), pp. 229-241.
    • (2006) J. Fluid Moch. , vol.560 , pp. 229-241
    • Doering, C.R.1    Otto, F.2    Reznikoff, M.G.3
  • 14
    • 38149144940 scopus 로고
    • On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation
    • C. FOIAS, M. JOLLY, I. G. KEVREKIDIS, AND E. S. TITI, On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation, Phys. Lett. A, 186 (1994), pp. 87-96.
    • (1994) Phys. Lett. A , vol.186 , pp. 87-96
    • Foias, C.1    Jolly, M.2    Kevrekidis, I.G.3    Titi, E.S.4
  • 17
    • 84968521933 scopus 로고
    • On the convergence of a time discretization scheme for the Navier-Stokes equations
    • T. GEVEOI, On the convergence of a time discretization scheme for the Navier-Stokes equations, Math. Comp., 53 (1989), pp. 43-53.
    • (1989) Math. Comp. , vol.53 , pp. 43-53
    • Geveoi, T.1
  • 18
    • 0033925498 scopus 로고    scopus 로고
    • Scaling in thermal convection: A unifying theory
    • S. GROSSMANN AND D. LOHSE, Scaling in thermal convection: A unifying theory, J. Fluid Moch., 407 (2000), pp. 27-56.
    • (2000) J. Fluid Moch. , vol.407 , pp. 27-56
    • Grossmann, S.1    Lohse, D.2
  • 21
    • 0022767064 scopus 로고
    • Finite element approximation of the nonstationary Navier-Stokes problem. II. Stability of solutions and error estimates uniform in time
    • J. G. HEYWOOD AND R. RANNAOHER, Finite element approximation of the nonstationary Navier-Stokes problem. II. Stability of solutions and error estimates uniform in time, SIAM J. Numer. Anal., 23 (1986), pp. 750-777.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 750-777
    • Heywood, J.G.1    Rannaoher, R.2
  • 22
    • 0034288886 scopus 로고    scopus 로고
    • Approximation of the global attractor for the incompressible NavierStokes equations
    • A. T. HILL AND E. SULI, Approximation of the global attractor for the incompressible NavierStokes equations, IMA J. Numer. Anal., 20 (2000), pp. 663-667.
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 663-667
    • Hill, A.T.1    Suli, E.2
  • 23
    • 5344252236 scopus 로고
    • Heat transport by turbulent convection
    • L. HOWARD, Heat transport by turbulent convection, J. Fluid Moch., 17 (1963), pp. 405-432.
    • (1963) J. Fluid Moch. , vol.17 , pp. 405-432
    • Howard, L.1
  • 24
    • 33748250252 scopus 로고    scopus 로고
    • Infinite-Prandtl-number convection. II. A singular limit of upper bound theory
    • G. R. IERLEY, R. R. KERSWELL, AND S. C. PLASTING, Infinite-Prandtl-number convection. II. A singular limit of upper bound theory, J. Fluid Moch., 560 (2006), pp. 159-227.
    • (2006) J. Fluid Moch. , vol.560 , pp. 159-227
    • Ierley, G.R.1    Kerswell, R.R.2    Plasting, S.C.3
  • 25
    • 0001630939 scopus 로고
    • Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation
    • M. JOLLY, I. KEVREKIDIS, AND E. S. TITI, Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation, J. Dynam. Differential Equations, 3 (1991), pp. 179-197.
    • (1991) J. Dynam. Differential Equations , vol.3 , pp. 179-197
    • Jolly, M.1    Kevrekidis, I.2    Titi, E.S.3
  • 26
    • 0036035323 scopus 로고    scopus 로고
    • On the global stability of a temporal discretization scheme for the Navier-Stokes equations
    • N. JU, On the global stability of a temporal discretization scheme for the Navier-Stokes equations, IMA J. Numer. Anal., 22 (2002), pp. 577-597.
    • (2002) IMA J. Numer. Anal. , vol.22 , pp. 577-597
    • Ju, N.1
  • 27
    • 0039567664 scopus 로고    scopus 로고
    • Turbulent heat flow: Structures and scaling
    • L. P. KADANOFF, Turbulent heat flow: Structures and scaling, Physics Today, 54 (2001), pp. 34- 39.
    • (2001) Physics Today , vol.54 , pp. 34-39
    • Kadanoff, L.P.1
  • 28
    • 0037944746 scopus 로고
    • The long-time behavior of finite-element approximations of solutions to semilinear parabolic problems
    • S. LARSSON, The long-time behavior of finite-element approximations of solutions to semilinear parabolic problems, SIAM J. Numer. Anal., 26 (1989), pp. 348-365.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 348-365
    • Larsson, S.1
  • 29
  • 30
  • 32
    • 0036789329 scopus 로고    scopus 로고
    • Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise
    • J. C. MATTINGLY, A. M. STUART, AND D. J. HIGHAM, Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise, Stochastic Process. Appl., 101 (2002), pp. 185-232.
    • (2002) Stochastic Process. Appl. , vol.101 , pp. 185-232
    • Mattingly, J.C.1    Stuart, A.M.2    Higham, D.J.3
  • 34
    • 0038815248 scopus 로고    scopus 로고
    • Global attractors in partial differential equations
    • North-Holland, Amsterdam
    • G. RAUGEL, Global attractors in partial differential equations, in Handbook of Dynamical Systems, Vol.2, North-Holland, Amsterdam, 2002, pp. 885-982.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 885-982
    • Raugel, G.1
  • 35
    • 0000920052 scopus 로고
    • Rigorous verification of trajectories for the computer simulation of dynamical systems
    • T. SAUER, AND J. A. YORKE, Rigorous verification of trajectories for the computer simulation of dynamical systems, Nonlinoarity, 4 (1991), pp. 961-979.
    • (1991) Nonlinoarity , vol.4 , pp. 961-979
    • Sauer, T.1    Yorke, J.A.2
  • 36
    • 0001092754 scopus 로고
    • Long time stability and convergence for the fully discrete nonlinear Galerkin methods
    • J. SHEN, Long time stability and convergence for the fully discrete nonlinear Galerkin methods, Appl. Anal., 38 (1990), pp. 201-229.
    • (1990) Appl. Anal. , vol.38 , pp. 201-229
    • Shen, J.1
  • 37
    • 4243254563 scopus 로고
    • High Rayleigh number convection
    • Annual Reviews, Palo Alto, CA
    • E. D. SIGGIA, High Rayleigh number convection, Annual Review of Fluid Mechanics, Vol.26, Annual Reviews, Palo Alto, CA, 1994, pp. 137-168.
    • (1994) Annual Review of Fluid Mechanics , vol.26 , pp. 137-168
    • Siggia, E.D.1
  • 40
    • 33847658879 scopus 로고    scopus 로고
    • On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations
    • F. TONE AND D. WIROSOETISNO, On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations, SIAM J. Numer. Anal., 44 (2006), pp. 29-40.
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 29-40
    • Tone, F.1    Wirosoetisno, D.2
  • 41
    • 0003987835 scopus 로고
    • 2nd od., Oxford Science Publications, Clarendon Press, Oxford University Press, Now York
    • D. J. TRITTON, Physical Fluid Dynamics, 2nd od., Oxford Science Publications, Clarendon Press, Oxford University Press, Now York, 1988.
    • (1988) Physical Fluid Dynamics
    • Tritton, D.J.1
  • 44
    • 4544241853 scopus 로고    scopus 로고
    • Infinite Prandtl number limit of Rayleigh-Bénard convection
    • X. WANG, Infinite Prandtl number limit of Rayleigh-Bénard convection, Comm. Pure Appl. Math., 57 (2004), pp. 1265-1282.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1265-1282
    • Wang, X.1
  • 45
    • 34547829711 scopus 로고    scopus 로고
    • Asymptotic behavior of global attractors to the Boussinesq system for RayleighBénard convection at large Prandtl number
    • X. WANG, Asymptotic behavior of global attractors to the Boussinesq system for RayleighBénard convection at large Prandtl number, Comm. Pure Appl. Math., 60 (2007), pp. 12931318.
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 12931318
    • Wang, X.1
  • 46
    • 52349104258 scopus 로고    scopus 로고
    • Stationary statistical properties of Rayleigh-Bénard convection at large Prandtl number
    • X. WANG, Stationary statistical properties of Rayleigh-Bénard convection at large Prandtl number, Comm. Pure Appl. Math., 61 (2008), pp. 789-815.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 789-815
    • Wang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.