메뉴 건너뛰기




Volumn 38, Issue 9, 2006, Pages 616-640

Uncertainty propagation in CFD using polynomial chaos decomposition

Author keywords

CFD; Navier Stokes; Numerical method; Polynomial chaos; Uncertainty quantification

Indexed keywords

ESTIMATION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; POLYNOMIALS; RANDOM PROCESSES;

EID: 33746436285     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fluiddyn.2005.12.003     Document Type: Article
Times cited : (251)

References (49)
  • 2
    • 0000139676 scopus 로고
    • 2 for the sparse representation of integral operators
    • 2 for the sparse representation of integral operators. SIAM J. Math. Anal. 24 (1993) 246-262
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 246-262
    • Alpert, B.K.1
  • 3
    • 0001308382 scopus 로고
    • Some basic hypergeometric polynomials that generalize Jacobi polynomials
    • Askey R., and Wilson J. Some basic hypergeometric polynomials that generalize Jacobi polynomials. Mem. Am. Math. Soc. 319 (1985)
    • (1985) Mem. Am. Math. Soc. , vol.319
    • Askey, R.1    Wilson, J.2
  • 4
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., and Martin W.T. The orthogonal development of nonlinear 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
  • 6
    • 0022514076 scopus 로고
    • Natural convection in an enclosed vertical layer with large horizontal temperature differences
    • Chenoweth D., and Paolucci S. Natural convection in an enclosed vertical layer with large horizontal temperature differences. J. Fluid Mech. 169 (1986) 173-210
    • (1986) J. Fluid Mech. , vol.169 , pp. 173-210
    • Chenoweth, D.1    Paolucci, S.2
  • 7
    • 40449093496 scopus 로고
    • A numerical method for solving incompressible viscous flow problems
    • Chorin A.J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2 (1967) 12-26
    • (1967) J. Comput. Phys. , vol.2 , pp. 12-26
    • Chorin, A.J.1
  • 8
    • 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) 387-403
    • (1970) J. Fluid Mech , vol.41 , pp. 387-403
    • Crow, S.C.1    Canavan, G.H.2
  • 10
    • 0041782621 scopus 로고    scopus 로고
    • Protein labeling reactions in electrochemical microchannel flow: numerical prediction and uncertainty propagation
    • Debusschere B., Najm H.N., Matta A., Knio O.M., Ghanem R.G., and Le Maître O.P. Protein labeling reactions in electrochemical microchannel flow: numerical prediction and uncertainty propagation. Phys. Fluids 15 8 (2003) 2238-2250
    • (2003) Phys. Fluids , vol.15 , Issue.8 , pp. 2238-2250
    • Debusschere, B.1    Najm, H.N.2    Matta, A.3    Knio, O.M.4    Ghanem, R.G.5    Le Maître, O.P.6
  • 11
    • 85140870121 scopus 로고    scopus 로고
    • Debusschere, B.J., Najm, H.N., Pébray, P.P., Knio, O.M., Ghanem, R.G., Le Maître, O.P., 2004. Numerical challenges in the use of polynomial chaos representations for stochastic processes. SIAM J. Sci. Comput. 26(2), 698-719.
  • 12
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite element formulation
    • Ghanem R. Ingredients for a general purpose stochastic finite element formulation. Comput. Methods Appl. Mech. Eng. 168 (1999) 19-34
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.168 , pp. 19-34
    • Ghanem, R.1
  • 13
    • 0032173318 scopus 로고    scopus 로고
    • Stochastic finite element analysis for multiphase flow in heterogeneous porous media
    • Ghanem R., and Dham S. Stochastic finite element analysis for multiphase flow in heterogeneous porous media. Transp. Porous Media 32 (1998) 239-262
    • (1998) Transp. Porous Media , vol.32 , pp. 239-262
    • Ghanem, R.1    Dham, S.2
  • 14
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous media
    • Ghanem R.G. Probabilistic characterization of transport in heterogeneous media. Comput. Methods Appl. Mech. Eng. 158 (1998) 199-220
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.158 , pp. 199-220
    • Ghanem, R.G.1
  • 15
    • 33746389651 scopus 로고    scopus 로고
    • Ghanem, R.G., Knio, O.M., 2000. A probabilistic framework for the validation and certification of computer simulations. In: Proceedings of 1st JANNAF Modeling and Simulation Subcommittee Meeting, 2000.
  • 16
    • 0029776146 scopus 로고    scopus 로고
    • Numerical solution of spectral stochastic finite element systems
    • Ghanem R.G., and Kruger R.M. Numerical solution of spectral stochastic finite element systems. Comput. Methods Appl. Mech. Eng. 129 (1996) 289-303
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.129 , pp. 289-303
    • Ghanem, R.G.1    Kruger, R.M.2
  • 17
    • 0026238497 scopus 로고
    • A spectral stochastic finite element formulation for reliability analysis
    • Ghanem R.G., and Spanos P.D. A spectral stochastic finite element formulation for reliability analysis. J. Eng. Mech. ASCE 117 (1991) 2351-2372
    • (1991) J. Eng. Mech. ASCE , vol.117 , pp. 2351-2372
    • Ghanem, R.G.1    Spanos, P.D.2
  • 19
    • 0031148476 scopus 로고    scopus 로고
    • Stochastic finite element modeling in linear transient heat transfer
    • Hien T.D., and Kleiber M. Stochastic finite element modeling in linear transient heat transfer. Comput. Methods Appl. Mech. Eng. 144 (1997) 111-124
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.144 , pp. 111-124
    • Hien, T.D.1    Kleiber, M.2
  • 21
    • 33746437959 scopus 로고    scopus 로고
    • Sparse quadrature as an alternative to Monte Carlo for stochastic finite element techniques
    • Keese A., and Matthies H.G. Sparse quadrature as an alternative to Monte Carlo for stochastic finite element techniques. Proc. Appl. Math. Mech. 3 1 (2003) 493-494
    • (2003) Proc. Appl. Math. Mech. , vol.3 , Issue.1 , pp. 493-494
    • Keese, A.1    Matthies, H.G.2
  • 22
    • 46549092989 scopus 로고
    • Application of a fractional-step method to incompressible Navier-Stokes equations
    • Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
    • (1985) J. Comput. Phys. , vol.59 , pp. 308-323
    • Kim, J.1    Moin, P.2
  • 23
    • 33746406043 scopus 로고    scopus 로고
    • Knio, O.M., Ghanem, R.G., 2001. Polynomial chaos product and moment formulas: a user utility. Technical Report, The Johns Hopkins University, Baltimore, MD, unpublished.
  • 24
    • 0035506770 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow. I. Basic formulation
    • Le Maître O.P., Knio O.M., Najm H.N., and Ghanem R.G. A stochastic projection method for fluid flow. I. Basic formulation. J. Comput. Phys. 173 (2001) 481-511
    • (2001) J. Comput. Phys. , vol.173 , pp. 481-511
    • Le Maître, O.P.1    Knio, O.M.2    Najm, H.N.3    Ghanem, R.G.4
  • 28
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • Le Maître O.P., Najm H.N., Ghanem R.G., and Knio O.M. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 197 2 (2004) 502-531
    • (2004) J. Comput. Phys. , vol.197 , Issue.2 , pp. 502-531
    • Le Maître, O.P.1    Najm, H.N.2    Ghanem, R.G.3    Knio, O.M.4
  • 29
    • 85140868470 scopus 로고    scopus 로고
    • Le Maître, O.P., Reagan, M.T., Debusschere, B., Najm, H.N., Ghanem, R.G., Knio, O.M., 2004c. Natural convection in a closed cavity under stochastic, non-Boussinesq conditions. SIAM J. Sci. Comput. 26 (2), 375-394.
  • 30
    • 0000213391 scopus 로고
    • A Chebychev collocation algorithm for 2d non-Boussinesq convection
    • Le Quéré P., Masson R., and Perror P. A Chebychev collocation algorithm for 2d non-Boussinesq convection. J. Comput. Phys. 103 (1992) 320-334
    • (1992) J. Comput. Phys. , vol.103 , pp. 320-334
    • Le Quéré, P.1    Masson, R.2    Perror, P.3
  • 33
    • 84948505075 scopus 로고
    • The derivation and numerical solution of the equations for zero-Mach number combustion
    • Majda A., and Sethian J. The derivation and numerical solution of the equations for zero-Mach number combustion. Combust. Sci. Technol. 42 (1985) 185-205
    • (1985) Combust. Sci. Technol. , vol.42 , pp. 185-205
    • Majda, A.1    Sethian, J.2
  • 34
    • 4344610300 scopus 로고    scopus 로고
    • Mathelin, L., Hussaini, M.Y., Zang, T.A., Bataille, F., 2004. Uncertainty propagation for turbulent compressible flow in a quasi-1d nozzle using stochastic methods. AIAA J. 42 (8), 1669-1676.
  • 35
    • 33746406698 scopus 로고    scopus 로고
    • Matta. A., 2003. Numerical Simulation and Uncertainty Quantification in Microfluidic systems. Ph.D. Thesis, Department of Civil Engineering, Johns Hopkins University.
  • 36
    • 33746425223 scopus 로고    scopus 로고
    • Matthies, H., Keese, A., 2003. Galerkins methods for linear and nonlinear elliptic stochastic partial differential equations. Report 2003-08, Institute of Scientific Computing, Technical University Braunschweig, Technical University Braunschweig Brunswick, Germany.
  • 37
    • 0031333532 scopus 로고    scopus 로고
    • Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite-elements
    • Matthies H.G., Brenner C.E., Bucher C.G., and Soares C.G. Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite-elements. Struct. Saf. 19 3 (1997) 283-336
    • (1997) Struct. Saf. , vol.19 , Issue.3 , pp. 283-336
    • Matthies, H.G.1    Brenner, C.E.2    Bucher, C.G.3    Soares, C.G.4
  • 38
    • 0018468345 scopus 로고
    • A comparison of three methods for selecting values of input variables in the analysis of output from a computer code
    • McKay M., Beckman R., and Conover W. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21 2 (1979) 239-245
    • (1979) Technometrics , vol.21 , Issue.2 , pp. 239-245
    • McKay, M.1    Beckman, R.2    Conover, W.3
  • 39
    • 0000476520 scopus 로고
    • Use of the Wiener-Hermite expansion for nearly normal turbulence
    • Meecham W.C., and Jeng D.T. Use of the Wiener-Hermite expansion for nearly normal turbulence. J. Fluid Mech. 32 (1968) 225
    • (1968) J. Fluid Mech. , vol.32 , pp. 225
    • Meecham, W.C.1    Jeng, D.T.2
  • 40
    • 33746469436 scopus 로고    scopus 로고
    • Najm, H.N., Reagan, M.T., Knio, O.M., Ghanem, R.G., Le Maître, O.P., 2003. Uncertainty quantification on reacting flow modelling. Technical Report 2003-8598, SANDIA.
  • 41
    • 0030524566 scopus 로고    scopus 로고
    • High-dimensional integration of smooth functions over cubes
    • Novak E., and Ritter K. High-dimensional integration of smooth functions over cubes. Numerische Math. 75 (1996) 79-97
    • (1996) Numerische Math. , vol.75 , pp. 79-97
    • Novak, E.1    Ritter, K.2
  • 42
    • 0009273790 scopus 로고    scopus 로고
    • The curse of dimension and a universal method for numerical integration
    • Nürnberger G., Schmidt J.W., and Walz G. (Eds), Birkhäuser, Basel
    • Novak E., and Ritter K. The curse of dimension and a universal method for numerical integration. In: Nürnberger G., Schmidt J.W., and Walz G. (Eds). Multivariate Approximation and Splines, ISNM (1997), Birkhäuser, Basel 177-188
    • (1997) Multivariate Approximation and Splines, ISNM , pp. 177-188
    • Novak, E.1    Ritter, K.2
  • 43
    • 0033238933 scopus 로고    scopus 로고
    • Simple cubature formulas with high polynomial exactness
    • Novak E., and Ritter K. Simple cubature formulas with high polynomial exactness. Constr. Approximation 15 (1999) 499-522
    • (1999) Constr. Approximation , vol.15 , pp. 499-522
    • Novak, E.1    Ritter, K.2
  • 44
    • 0035606625 scopus 로고    scopus 로고
    • Fast calculation of coefficients in the Smolyak algorithm
    • Petras K. Fast calculation of coefficients in the Smolyak algorithm. Numer. Algorithms 26 (2001) 93-109
    • (2001) Numer. Algorithms , vol.26 , pp. 93-109
    • Petras, K.1
  • 45
    • 0030735572 scopus 로고    scopus 로고
    • Incorporation of parametric uncertainty into complex kinetic mechanisms: application to hydrogen oxidation in supercritical water
    • Phenix B.D., Dinaro J.L., Tatang M.A., Tester J.W., Howard J.B., and McRae G.J. Incorporation of parametric uncertainty into complex kinetic mechanisms: application to hydrogen oxidation in supercritical water. Combust. Flame 112 (1998) 132-146
    • (1998) Combust. Flame , vol.112 , pp. 132-146
    • Phenix, B.D.1    Dinaro, J.L.2    Tatang, M.A.3    Tester, J.W.4    Howard, J.B.5    McRae, G.J.6
  • 46
    • 0001048297 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions
    • Smolyak S.A. Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 4 (1963) 240-243
    • (1963) Dokl. Akad. Nauk SSSR , vol.4 , pp. 240-243
    • Smolyak, S.A.1
  • 47
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener S. The homogeneous chaos. Am. J. Math. 60 (1938) 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, S.1
  • 48
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D.B., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. J. Sci. Comput. 24 (2002) 619-644
    • (2002) J. Sci. Comput. , vol.24 , pp. 619-644
    • Xiu, D.B.1    Karniadakis, G.E.2
  • 49
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D.B., 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.B.1    Karniadakis, G.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.