Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics

Annual Review of Fluid Mechanics - Tập 41 Số 1 - Trang 35-52 - 2009
Habib N. Najm1
1Sandia National Laboratories, Livermore, California 94551

Tóm tắt

The quantification of uncertainty in computational fluid dynamics (CFD) predictions is both a significant challenge and an important goal. Probabilistic uncertainty quantification (UQ) methods have been used to propagate uncertainty from model inputs to outputs when input uncertainties are large and have been characterized probabilistically. Polynomial chaos (PC) methods have found increased use in probabilistic UQ over the past decade. This review describes the use of PC expansions for the representation of random variables/fields and discusses their utility for the propagation of uncertainty in computational models, focusing on CFD models. Many CFD applications are considered, including flow in porous media, incompressible and compressible flows, and thermofluid and reacting flows. The review examines each application area, focusing on the demonstrated use of PC UQ and the associated challenges. Cross-cutting challenges with time unsteadiness and long time horizons are also discussed.

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Tài liệu tham khảo

10.1090/memo/0319

10.1016/j.jcp.2005.02.007

10.1137/S0036142902418680

10.1137/050645142

Bear J, 1972, Dynamics of Fluids in Porous Media

10.2307/2006396

10.1201/9780203498798

10.1017/S0962492900002804

10.2307/1969178

10.1016/j.jcp.2004.10.019

10.1017/S0022112074000991

Cox E, 1999, The Fuzzy Systems Handbook: A Practitioner's Guide to Building, Using, and Maintaining Fuzzy Systems, 2

10.1017/S0022112070000654

10.2307/2669939

Das S, Ghanem R, Spall J. 2008. Asymptotic sampling distribution for polynomial chaos representation from data: a maximum entropy and Fisher information approach. SIAM J. Sci. Comput. In press

10.1016/S0045-7825(01)00237-7

10.1063/1.1582857

10.1137/S1064827503427741

10.1142/2775

Faragher J. 2004. Probabilistic methods for the quantification of uncertainty and error in computational fluid dynamics simulations. Tech. Rep. DSTO-TR-1633, Aust. Gov., Dept. Def., Def. Sci. Tech. Org.

10.1016/j.jcp.2006.12.014

10.1115/1.2791894

10.1016/S0045-7825(97)00250-8

10.1023/A:1006514109327

10.1007/978-1-4612-3094-6

10.1016/j.jcp.2006.01.037

10.1061/(ASCE)0733-9399(2002)128:1(66)

Hansen E, 1992, Global Optimization Using Interval Analysis

10.1016/j.ress.2004.03.025

Hosder S, Walters R, Balch M. 2008. Efficient uncertainty quantification applied to the aeroelastic analysis of a transonic wing. Presented at AIAA Aerosp. Sci. Meet. Exhib, Reno, 46th, Art. No. AIAA-2008-729

Hosder S, Walters R, Perez R. 2006. A nonintrusive polynomial chaos method for uncertainty propagation in CFD simulations. Presented at AIAA Aerosp. Sci. Meet. Exhib, 44th, Reno, Art. No. AIAA-2006-0891

10.1016/j.jcp.2006.01.008

10.1111/j.1539-6924.1998.tb01301.x

10.1017/CBO9780511526169

10.1017/CBO9780511790423

Karhunen K, 1946, Ann. Acad. Sci. Fennicae, 34, 1

10.1016/j.fluiddyn.2005.12.003

Kozine I. 1999. Imprecise probabilities relating to prior reliability assessments. Presented at Int. Symp. Imprecise Probab. Appl., 1st, Ghent, Belgium

10.1016/j.crme.2006.10.001

10.1016/j.jcp.2003.11.033

10.1016/j.jcp.2007.04.030

10.1006/jcph.2001.6889

10.1016/j.jcp.2003.12.020

10.1137/050643118

10.1137/S1064827503422853

10.1006/jcph.2002.7104

10.1016/S0266-8920(97)00020-9

10.1016/j.jcp.2006.02.009

Loève M, 1948, Processus Stochastiques et Movement Brownien

10.1137/S1064827503426826

10.1103/PhysRevLett.92.154501

Mathelin L, Hussaini M. 2003. A stochastic collocation algorithm for uncertainty analysis. NASA Tech. Rep. NASA/CR-2003–212153, Langley Res. Cent., Hampton, Va.

10.1007/BF02810624

Mathelin L, Hussaini M, Zang T, Bataille F. 2003. Uncertainty propagation for turbulent, compressible flow in a quasi-1D nozzle using stochastic methods. Presented at AIAA Comput. Fluid Dyn. Conf., 69th, Orlando, Art. No. AIAA-2003-4240

10.2514/1.5674

10.1016/j.cma.2004.05.027

10.1016/j.jcp.2004.06.019

Nobile F, Tempone R, Webster C. 2008a. An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. In press

Nobile F, Tempone R, Webster C. 2008b. A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. In press

10.2514/2.456

Oberkampf W, 2005, Engineering Design Reliability Handook

10.1063/1.1762082

Perez R, Walters R. 2005. An implicit polynomial chaos formulation for the Euler equations. Presented at AIAA Aerosp. Sci. Meet. Exhib, 43rd, Reno, Art. No. AIAA-2005-1406

Pettit C, Beran P. 2004. Polynomial chaos expansions applied to airfoil limit cycle oscillations. Presented at AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn., Mater. Conf., 45th, Palm Springs, Art. No. AIAA-2004-1691

10.1016/j.jsv.2005.12.043

10.1016/S0010-2180(97)81762-2

10.1088/1364-7830/8/3/010

10.1016/S0010-2180(02)00503-5

10.1002/kin.20081

10.1214/aoms/1177729394

Saltelli A, 2000, Sensitivity Analysis

10.1007/978-1-4612-1170-9

Smoljak SA, 1963, Soviet Math. Dokl., 4, 240

10.1137/S1064827503424505

10.1016/j.jcp.2006.02.029

Tatang M, 1995, Direct incorporation of uncertainty in chemical and environmental engineering systems

Walters R, Huyse L. 2002. Uncertainty analysis for fluid mechanics with applications. ICASE Rep. No. 2002-1; NASA/CR-2002-211449, Langley Res. Cent., Hampton, Va.

10.1016/j.cma.2005.10.016

10.1137/050627630

10.1016/j.jcp.2005.03.023

10.1023/A:1005685317358

10.2307/2371268

Wiener N, 1939, Proc. Fifth Int. Cong. Appl. Mech., 356

10.1137/040615201

10.1137/S1064827501387826

10.1016/S0021-9991(03)00092-5

10.1115/1.1436089

Zang T, Hemsch M, Hilburger M, Kenny S, Luckring J, et al. 2002. Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles. Tech. Rep. NASA/TM-2002-211462, Langley Res. Cent., Hampton, Va.