메뉴 건너뛰기




Volumn 216, Issue 2, 2006, Pages 687-706

Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

Author keywords

Navier Stokes equations; Numerical methods; Stochastic differential equations; Wiener Chaos expansions

Indexed keywords

BROWNIAN MOVEMENT; INTELLIGENT SYSTEMS; MONTE CARLO METHODS; NUMERICAL METHODS; STOCHASTIC SYSTEMS; VISCOUS FLOW;

EID: 33744543472     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.01.008     Document Type: Article
Times cited : (183)

References (30)
  • 2
    • 0001159580 scopus 로고
    • Equations stochastiques du type Navier-Stokes
    • Bensoussan A., and Temam R. Equations stochastiques du type Navier-Stokes. J. Func. Anal. 13 (1973) 195-222
    • (1973) J. Func. Anal. , vol.13 , pp. 195-222
    • Bensoussan, A.1    Temam, R.2
  • 3
    • 0000148817 scopus 로고
    • The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., and Martin W.T. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Ann. Math. 48 (1947) 385-392
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 5
    • 0042885804 scopus 로고    scopus 로고
    • Ergodicity for the 3D stochastic Navier-Stokes equations
    • Da Prato G., and Debussche A. Ergodicity for the 3D stochastic Navier-Stokes equations. J. Math. Pure Appl. 82 (2003) 877-947
    • (2003) J. Math. Pure Appl. , vol.82 , pp. 877-947
    • Da Prato, G.1    Debussche, A.2
  • 6
    • 0001203226 scopus 로고
    • Hermite expansion in Monte-Carlo simulations
    • Chorin A.J. Hermite expansion in Monte-Carlo simulations. J. Comput. Phys. 8 (1971) 472-482
    • (1971) J. Comput. Phys. , vol.8 , pp. 472-482
    • Chorin, A.J.1
  • 7
    • 0347659106 scopus 로고
    • Gaussian fields and random flow
    • Chorin A.J. Gaussian fields and random flow. J. Fluid Mech. 63 (1974) 21-32
    • (1974) J. Fluid Mech. , vol.63 , pp. 21-32
    • Chorin, A.J.1
  • 9
    • 0014765554 scopus 로고
    • Relationship between a Wiener-Hermite expansion and an energy cascade
    • Crow S.C., and Canavan G.H. Relationship between a Wiener-Hermite expansion and an energy cascade. J. Fluid Mech. 41 (1970) 387
    • (1970) J. Fluid Mech. , vol.41 , pp. 387
    • Crow, S.C.1    Canavan, G.H.2
  • 13
    • 1142296114 scopus 로고    scopus 로고
    • Spectral polynomial chaos solutions of the stochastic advection equation
    • Jardak M., Su C.H., and Karniadakis G.E. 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
  • 15
    • 6244236583 scopus 로고    scopus 로고
    • Probability distribution functions for the random forced Burgers equation
    • Khanin W.E.K., Mazel A., and Sinai Ya. Probability distribution functions for the random forced Burgers equation. Phys. Rev. Lett. 78 (1997) 1904-1907
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 1904-1907
    • Khanin, W.E.K.1    Mazel, A.2    Sinai, Ya.3
  • 16
    • 0034347507 scopus 로고    scopus 로고
    • Invariant measures for Burgers equation with stochastic forcing
    • Khanin W.E.K., Mazel A., and Sinai Ya. Invariant measures for Burgers equation with stochastic forcing. Ann. Math. 151 (2000) 877-960
    • (2000) Ann. Math. , vol.151 , pp. 877-960
    • Khanin, W.E.K.1    Mazel, A.2    Sinai, Ya.3
  • 17
    • 33646950376 scopus 로고
    • Small-scale structure of a scalar field convected by turbulence
    • Kraichnan R.H. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11 (1968) 487-489
    • (1968) Phys. Fluids , vol.11 , pp. 487-489
    • Kraichnan, R.H.1
  • 18
    • 0032045223 scopus 로고    scopus 로고
    • Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration
    • Li R., and Ghanem R. Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration. Prob. Eng. Mech. 13 (1998) 125-136
    • (1998) Prob. Eng. Mech. , vol.13 , pp. 125-136
    • Li, R.1    Ghanem, R.2
  • 20
    • 0011004706 scopus 로고
    • High-order and efficient methods for the vorticity formulation of the Euler equations
    • Lowengrub J.S., Shelley M.J., and Merriman B. High-order and efficient methods for the vorticity formulation of the Euler equations. SIAM J. Sci. Comput. 14 (1993) 1107-1142
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1107-1142
    • Lowengrub, J.S.1    Shelley, M.J.2    Merriman, B.3
  • 21
    • 16244411330 scopus 로고    scopus 로고
    • Adaptive generalized polynomial chaos for nonlinear random oscillators
    • Lucor D., and Karniadakis G.E. Adaptive generalized polynomial chaos for nonlinear random oscillators. SIAM J. Sci. Comput. 26 2 (2004) 720-735
    • (2004) SIAM J. Sci. Comput. , vol.26 , Issue.2 , pp. 720-735
    • Lucor, D.1    Karniadakis, G.E.2
  • 23
    • 1842643758 scopus 로고    scopus 로고
    • Stochastic Navier-Stokes equations for turbulence flow
    • Mikulevicius R., and Rozovskii B. Stochastic Navier-Stokes equations for turbulence flow. SIAM J. Math. Anal. 35 (2004) 1250-1310
    • (2004) SIAM J. Math. Anal. , vol.35 , pp. 1250-1310
    • Mikulevicius, R.1    Rozovskii, B.2
  • 24
    • 0013201448 scopus 로고
    • Dynamical properties of truncated Wiener-Hermite expansions
    • Orszag S.A., and Bissonnette L.R. Dynamical properties of truncated Wiener-Hermite expansions. Phys. Fluids 10 (1967) 2603
    • (1967) Phys. Fluids , vol.10 , pp. 2603
    • Orszag, S.A.1    Bissonnette, L.R.2
  • 25
    • 0003003979 scopus 로고
    • Wave propagation in a one-dimensional random medium
    • Papanicolaou G. Wave propagation in a one-dimensional random medium. SIAM J. Appl. Math. 21 (1971) 13-18
    • (1971) SIAM J. Appl. Math. , vol.21 , pp. 13-18
    • Papanicolaou, G.1
  • 26
    • 0000471035 scopus 로고
    • Diffusion in random media
    • Keller J.B., McLaughlin D., and Papanicolaou G. (Eds), Plenum Press, New York
    • Papanicolaou G. Diffusion in random media. In: Keller J.B., McLaughlin D., and Papanicolaou G. (Eds). Surveys in Applied Mathematics (1995), Plenum Press, New York 205-255
    • (1995) Surveys in Applied Mathematics , pp. 205-255
    • Papanicolaou, G.1
  • 27
    • 0036472444 scopus 로고    scopus 로고
    • Polynomial chaos decomposition for the simulation of non-Gaussian non-stationary stochastic processes
    • Sakamoto S., and Ghanem R. Polynomial chaos decomposition for the simulation of non-Gaussian non-stationary stochastic processes. J. Eng. Mech. 128 (2002) 190-201
    • (2002) J. Eng. Mech. , vol.128 , pp. 190-201
    • Sakamoto, S.1    Ghanem, R.2
  • 28
    • 1442307688 scopus 로고    scopus 로고
    • An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansion
    • Zhang D., and Lu Z. An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansion. J. Comput. Phys. 194 (2004) 773-794
    • (2004) J. Comput. Phys. , vol.194 , pp. 773-794
    • Zhang, D.1    Lu, Z.2
  • 29
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. 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
  • 30
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput 24 (2002) 619-644
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.