Fishman,
G.
, 2013, Monte Carlo: Concepts, Algorithms, and Applications,
Springer Science & Business Media,
New York.

Ghanem,
R. G.
, and
Spanos,
P. D.
, 2003, Stochastic Finite Elements: A Spectral Approach,
Courier Corporation,
Mineola, New York.

Wiener,
N.
, 1938, “
The Homogeneous Chaos,” Am. J. Math.,
60(4), pp. 897–936.

[CrossRef]
Ghanem,
R.
, and
Kruger,
R. M.
, 1996, “
Numerical Solution of Spectral Stochastic Finite Element Systems,” Comput. Methods Appl. Mech. Eng.,
129(3), pp. 289–303.

[CrossRef]
Ghanem,
R.
, 1999, “
Ingredients for a General Purpose Stochastic Finite Elements Implementation,” Comput. Methods Appl. Mech. Eng.,
168(1–4), pp. 19–34.

[CrossRef]
Ghanem,
R.
, 1999, “
Stochastic Finite Elements With Multiple Random Non-Gaussian Properties,” J. Eng. Mech.,
125(1), pp. 26–40.

[CrossRef]
Ghanem,
R.
, and
Red-Horse,
J.
, 1999, “
Propagation of Probabilistic Uncertainty in Complex Physical Systems Using a Stochastic Finite Element Approach,” Physica D,
133(1–4), pp. 137–144.

[CrossRef]
Debusschere,
B. J.
,
Najm,
H. N.
,
Pebay,
P. P.
,
Knio,
O. M.
,
Ghanem,
R. G.
, and
Maitre,
O. P. L.
, 2004, “
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes,” SIAM J. Sci. Comput.,
26(2), pp. 698–719.

[CrossRef]
Reagana,
M. T.
,
Najm,
H. N.
,
Ghanem,
R. G.
, and
Knio,
O. M.
, 2003, “
Uncertainty Quantification in Reacting-Flow Simulations Through Non-Intrusive Spectral Projection,” Combust. Flame,
132(3), pp. 545–555.

[CrossRef]
Mathelin,
L.
,
Hussaini,
M. Y.
, and
Zang,
T. A.
, 2005, “
Stochastic Approaches to Uncertainty Quantification in CFD Simulations,” Numer. Algorithms,
38(1–3), pp. 209–236.

[CrossRef]
Hosder,
S.
,
Walters,
R. W.
, and
Perez,
R.
, 2006, “
A Non-Intrusive Polynomial Chaos Method for Uncertainty Propagation in CFD Simulations,” AIAA Paper No. 2006-891.

Hosder,
S.
,
Walters,
R. W.
, and
Balch,
M.
, 2008, “
Efficient Uncertainty Quantification Applied to the Aeroelastic Analysis of a Transonic Wing,” AIAA Paper No. 2008-729.

Bettis,
B. R.
, and
Hosder,
S.
, 2010, “
Quantification of Uncertainty in Aerodynamic Heating of a Reentry Vehicle Due to Uncertain Wall and Freestream Conditions,” AIAA 2010-4642.

Raisee,
M.
,
Kumar,
D.
, and
Lacor,
C.
, 2015, “
A Non-Intrusive Model Reduction Approach for Polynomial Chaos Expansion Using Proper Orthogonal Decomposition,” Int. J. Numer. Methods Eng.,
103(4), pp. 293–312.

[CrossRef]
Najm,
H. N.
, 2009, “
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics,” Annu. Rev. Fluid Mech.,
41(1), pp. 35–52.

[CrossRef]
Loeven,
G. J. A.
, and
Bijl,
H.
, 2010, “
The Application of the Probabilistic Collocation Method to a Transonic Axial Flow Compressor,” AIAA Paper No. 2010-2923.

Petrone,
G.
,
De Nicola,
C.
,
Quagliarella,
D.
,
Witteveen,
J.
, and
Iaccarino,
G.
, 2011, “
Wind Turbine Performance Analysis Under Uncertainty,” AIAA Paper No. 2011-544.

Liu,
Z.
,
Wang,
X.
, and
Kang,
S.
, 2014, “
Stochastic Performance Evaluation of Horizontal Axis Wind Turbine Blades Using Non-Deterministic CFD Simulations,” Energy,
73, pp. 126–136.

[CrossRef]
Pečnik,
R.
,
Witteveen,
J. A.
, and
Iaccarino,
G.
, 2011, “
Uncertainty Quantification for Laminar-Turbulent Transition Prediction in RANS Turbomachinery Applications,” AIAA Paper No. 2011-660.

Gopinathrao,
N. P.
,
Mabilat,
C.
, and
Alizadeh,
S.
, 2009, “
Non-Deterministic Thermo-Fluid Analysis of a Compressor Rotor-Stator Cavity,” AIAA Paper No. 2009-2278.

Han,
X.
,
Sagaut,
P.
, and
Lucor,
D.
, 2012, “
On Sensitivity of RANS Simulations to Uncertain Turbulent Inflow Conditions,” Comput. Fluids,
61, pp. 2–5.

[CrossRef]
Congedo,
P. M.
,
Duprat,
C.
,
Balarac,
G.
, and
Corre,
C.
, 2013, “
Numerical Prediction of Turbulent Flows Using Reynolds-Averaged Naiver–Stokes and Large-Eddy Simulation With Uncertain Inflow Conditions,” Int. J. Numer. Methods Fluids,
72(3), pp. 341–358.

[CrossRef]
Ko,
J.
,
Lucor,
D.
, and
Sagaut,
P.
, 2008, “
Sensitivity of Two-Dimensional Spatially Developing Mixing Layers With Respect to Uncertain Inflow Conditions,” Phys. Fluids,
20(7), p. 077102.

[CrossRef]
Abdelaziz,
O.
, and
Radermacher,
R.
, 2010, “
Modeling Heat Exchangers Under Consideration of Manufacturing Tolerances and Uncertain Flow Distribution,” Int. J. Refrig.,
33(4), pp. 815–828.

[CrossRef]
Han,
X.
,
Sagaut,
P.
,
Lucor,
D.
, and
Afgan,
I.
, 2012, “
Stochastic Response of the Laminar Flow Past a Flat Plate Under Uncertain Inflow Conditions,” Int. J. Comput. Fluid Dyn.,
26(2), pp. 101–117.

[CrossRef]
García-Sánchez,
C.
,
Philips,
D.
, and
Gorlé,
C.
, 2014, “
Quantifying Inflow Uncertainties for CFD Simulations of the Flow in Downtown Oklahoma City,” Build. Environ.,
78, pp. 118–129.

[CrossRef]
Cervantes,
M.
, and
Engstrom,
T.
, 2008, “
Pulsating Turbulent Flow in a Straight Asymmetric Diffuser,” J. Hydraul. Res.,
46(1), pp. 112–128.

[CrossRef]
Salehi,
S.
, 2013, “
Computation of Developing Turbulent Flow Through a Straight Asymmetric Diffuser With Moderate Adverse Pressure Gradient,” Master's thesis, University of Tehran, Tehran, Iran.

Durst,
F.
,
Fischer,
M.
,
Jovanović,
J.
, and
Kikura,
H.
, 1998, “
Methods to Setup and Investigate Low Reynolds Number, Fully Developed Turbulent Plane Channel Flows,” ASME J. Fluids Eng.,
120(3), pp. 496–503.

[CrossRef]
Kaltenback,
H.
,
Fatica,
M.
,
Mittal,
R.
,
Lund,
T.
, and
Moin,
P.
, 1999, “
Study of the Flow in a Planar Asymmetric Diffuser Using Large Eddy Simulations,” J. Fluid Mech.,
390, pp. 151–185.

[CrossRef]
Sbrizzai,
F.
,
Verzicco,
R.
, and
Soldati,
A.
, 2009, “
Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe,” Flow, Turbul. Combust.,
82(1), pp. 1–23.

[CrossRef]
Wang,
L.
, 2008, “
Karhunen–Loève Expansions and Their Applications,” Ph.D. thesis, London School of Economics and Political Science, UK.

Launder,
B.
, and
Sharma,
B.
, 1974, “
Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc,” Lett. Heat Mass Transfer,
1(2), pp. 131–137.

[CrossRef]
Weller,
H. G.
,
Tabor,
G.
,
Jasak,
H.
, and
Fureby,
C.
, 1998, “
A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques,” Comput. Phys.,
12(6), pp. 620–631.

[CrossRef]
Xiu,
D.
, and
Karniadakis,
G.
, 2002, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM J. Sci. Comput.,
24(2), pp. 619–644.

[CrossRef]
Witteveen,
J. A.
, and
Bijl,
H.
, 2006, “
Modeling Arbitrary Uncertainties Using Gram–Schmidt Polynomial Chaos,” AIAA Paper No. 2006-896.

Sudret,
B.
, 2008, “
Global Sensitivity Analysis Using Polynomial Chaos Expansions,” Reliab. Eng. Syst. Saf.,
93(7), pp. 964–979.

[CrossRef]
Hosder,
S.
,
Walters,
R. W.
, and
Balch,
M.
, 2007, “
Efficient Sampling for Non-Intrusive Polynomial Chaos Applications With Multiple Input Uncertain Variables,” AIAA Paper No. 2007-1939.

Sobol’,
I.
, 1990, “
On Sensitivity Estimation for Nonlinear Mathematical Models,” Mat. Model.,
2(1), pp. 112–118.

Obi,
S.
,
Aoki,
K.
, and
Masuda,
S.
, 1993, “
Experimental and Computational Study of Turbulent Separating Flow in an Asymmetric Plane Diffuser,” Ninth Symposium on Turbulent Shear Flows, Kyoto, Japan, Aug. 16–18, pp. 305.1–305.4.

Buice,
C.
, and
Eaton,
J.
, 2000, “
Experimental Investigation of Flow Through an Asymmetric Plane Diffuser,” ASME J. Fluids Eng.,
122(2), pp. 433–435.

[CrossRef]
Iaccarino,
G.
, 2001, “
Prediction of a Turbulent Separated Flow Using Commercial CFD Codes,” ASME J. Fluids Eng.,
123(4), pp. 819–828.

[CrossRef]
El-Behery,
S. M.
, and
Hamed,
M. H.
, 2011, “
A Comparative Study of Turbulence Models Performance for Separating Flow in a Planar Asymmetric Diffuser,” Comput. Fluids,
44(1), pp. 248–257.

[CrossRef]
Durbin,
P. A.
, 1995, “
Separated Flow Computations With the

*k*–

*ε*–

*v*^{2} Model,” AIAA J.,
33(4), pp. 659–664.

[CrossRef]
Loh,
W. L.
, 1996, “
On Latin Hypercube Sampling,” Ann. Stat.,
24(5), pp. 2058–2080.

[CrossRef]