Uncertainty Propagation for a Turbulent, Compressible Nozzle Flow Using Stochastic Methods

A fully spectral, polynomial chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow is described. The method is applied to the flow in a quasi-one-dimensional nozzle. Results demonstrate the ability of the method to propagate accurately the uncertainty throughout the entire numerical field. Comparison and validation were made with the reference Monte Carlo method. An exact method and an approximate method for the computation of inner products are also discussed in terms of efficiency and number of operations required

[1]  Patrick Roache,et al.  Error Bars for CFD , 2003 .

[2]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[3]  Roger Ghanem,et al.  Ingredients for a general purpose stochastic finite elements implementation , 1999 .

[4]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[5]  Robert E. Childs,et al.  Best Practices for Reduction of Uncertainty in CFD Results , 2003 .

[6]  Sean P. Kenny,et al.  Needs and Opportunities for Uncertainty- Based Multidisciplinary Design Methods for Aerospace Vehicles , 2002 .

[7]  D. Xiu,et al.  Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos , 2002 .

[8]  U. B. Mehta,et al.  Some Aspects of Uncertainty in Computational Fluid Dynamics Results , 1991 .

[9]  R. Ghanem,et al.  A stochastic projection method for fluid flow. I: basic formulation , 2001 .

[10]  Jun Shao,et al.  Statistical Approach to CFD Code Certification , 2003 .

[11]  William L. Oberkampf,et al.  Issues in Computational Fluid Dynamics Code Verification and Validation , 1997 .

[12]  N. Wiener.  The Homogeneous Chaos , 1938 .

[13]  Timothy G. Trucano,et al.  Verification and Validation in Computational Fluid Dynamics , 2002 .

[14]  Edwrd Tinoco,et al.  Minimizing CFD Uncertainty for Commercial Aircraft Applications (Invited) , 2003 .

[15]  M. Yousuff Hussaini,et al.  Exploitation of Sensitivity Derivatives for Improving Sampling Methods , 2003 .

[16]  Hugh W. Coleman,et al.  Uncertainties and CFD Code Validation , 1997 .

[17]  Gusheng Hu,et al.  FURTHER REFINEMENT AND BENCH MARKING OF A SINGLE-GRID ERROR ESTIMATION TECHNIQUE , 2003 .

[18]  H. Najm,et al.  A stochastic projection method for fluid flow II.: random process , 2002 .

[19]  M. Yousuff Hussaini,et al.  Uncertainty Quantification in CFD Simulations: A Stochastic Spectral Approach , 2003 .

[20]  Christopher J. Roy,et al.  Discretization Error Estimates Using Exact Solutions to Nearby Problems , 2003 .

[21]  Michael J. Hemsch,et al.  Statistical Analysis of Computational Fluid Dynamics Solutions from the Drag Prediction Workshop , 2004 .

[22]  O. L. Maître,et al.  Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation , 2003 .

[23]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[24]  L. Mathelin,et al.  A Stochastic Collocation Algorithm for Uncertainty Analysis , 2003 .

[25]  Raymond Cosner.  The Importance of Uncertainty Estimation in Computational Fluid Dynamics (Invited) , 2003 .

[26]  Roger W. Logan,et al.  Validation, Uncertainty, and Quantitative Reliability at Confidence (QRC) , 2003 .

[27]  O. L. Maître,et al.  Uncertainty propagation in CFD using polynomial chaos decomposition , 2006 .

[28]  Joseph H. Morrison,et al.  Uncertainty in Computational Aerodynamics , 2003 .

[29]  Jon C. Helton,et al.  Mathematical representation of uncertainty , 2001 .

[30]  Michael J. Hemsch,et al.  Statistical Analysis of CFD Solutions from the Drag Prediction Workshop , 2002 .

[31]  François M. Hemez,et al.  UNCERTAINTY QUANTIFICATION OF SIMULATION CODES BASED ON EXPERIMENTAL DATA , 2003 .

[32]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .