Comparison of the Point-Collocation Non-Intrusive Polynomial (NIPC) and Non-Intrusive Spectral Projection (NISP) Methods for the γ − R θ Transition Model
Source abstract
Abstract
In the present work, a comparative study of two major non-intrusive polynomial chaos methods, Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) and Non-Intrusive Spectral Projection (NISP), was conducted for the transitional γ − R θ transitional model. Three multiple model coefficients, Ca2, Ce1, and Ce2 were considered with multiple random inputs with the assumption of uniform distributions with ±10% deviation. The target transitional flows were one around a flat plate and Aerospatiale A-airfoil. Deterministic solutions were obtained by employing the open source software OpenFOAM. The results of two methods were compared to the results of Monte Carlo simulation with 500 runs. The order convergence of the mean value and the standard deviation (STD) were compared in terms of the quantities of interest, drag and lift coefficients. Further, the most effective model coefficient for each transitional flow could be found through the calculation of the Sobol index.
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Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Wind and Air Flow Studies · Computational Fluid Dynamics and Aerodynamics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Mechanical and Automotive Engineering, University of Ulsan; Ulsan 44610, Korea
References (36)
Show source-provided references
1. Polynomial chaos in stochastic finite elements10.1115/1.2888303 ↗
2. Ghanem, R. (1999). Stochastic finite elements with multiple random non-Gaussian properties. J. Eng. Mech., 26–40.10.1061/(ASCE)0733-9399(1999)125:1(26) ↗
3. Ingredient for a general purpose stochastic finite element formulation10.1016/S0045-7825(98)00106-6 ↗
4. Uncertainty propagation for turbulent, compressible nozzle flow using stochastic methods10.2514/1.5674 ↗
5. Numerical challenges in the use of polynomial chaos representations for stochastic processes10.1137/S1064827503427741 ↗
6. Uncertainty quantification in reacting flow simulations through non-intrusive spectral projection10.1016/S0010-2180(02)00503-5 ↗
7. Stochastic approaches to uncertainty quantification in CFD simulations10.1007/s11075-004-2866-z ↗
8. The homogeneous chaos10.2307/2371268 ↗
9. The discrete chaos10.2307/2371816 ↗
10. Uncertainty propagation in CFD using polynomial chaos decomposition10.1016/j.fluiddyn.2005.12.003 ↗
11. The Wiener-Askey polynomial chaos for stochastic differential equation
12. Modeling uncertainty in flow simulations via generalized polynomial chaos10.1016/S0021-9991(03)00092-5 ↗
13. A k-ε-γ equation turbulence model10.1017/S0022112092003422 ↗
14. The role of laminar-Turbulence modeling of by-pass transition10.1115/1.2929110 ↗
15. Xiu, D. (2010). Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press.10.1515/9781400835348 ↗
16. Hosder, S., Walters, R., and Balch, M. (2007, January 23–26). Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables. Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, HI, USA. AIAA 2007-1939.10.2514/6.2007-1939 ↗
17. Hosder, S., Walters, R., and Perez, R. (2006, January 9–12). A Non-Intrusive Polynomial Chaos Method for Uncertainty Propagation in CFD Simulations. Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA. AIAA 2006-891.10.2514/6.2006-891 ↗
18. Loeven, G.J.A., Witteveen, J.A.S., and Bijl, H. (2007, January 8–11). Probabilistic Collocation: An Efficient Non-Intrusive Approach for Arbitrarily Distributed Parametric Uncertainties. Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA. AIAA 2007-317.10.2514/6.2007-317 ↗
19. Platteeuw, P.D.A., Loeven, G.J.A., and Bijl, H. (2008, January 7–10). Uncertainty quantification applied to the k-epsilon model of turbulence using the probabilistic collocation model. Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Schaumburg, IL, USA.10.2514/6.2008-2150 ↗
20. Uncertainty quantification of turbulence model coefficients for transonic wall-bounded flow10.2514/1.J054902 ↗
21. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics Codes10.2514/1.42362 ↗
22. Two-equation eddy-viscosity turbulence models for engineering application10.2514/3.12149 ↗
23. Viscous-inviscid analysis of transonic and low Reynolds number airfoils10.2514/3.9789 ↗
24. Prediction of high-lift flows using turbulent closure models10.2514/2.435 ↗
25. Sullivan, T.J. (2015). Introduction to Uncertainty Quantification, Springer.10.1007/978-3-319-23395-6 ↗
26. Bijl, H., Lucor, D., Mishra, S., and Schwab, C. (2013). Implementation of Intrusive Polynomial Chaos in CFD Codes and Application to 3D Navier-Stokes. Uncertainty Quantification in Computational Fluid Dynamics, Springer.10.1007/978-3-319-00885-1_5 ↗
27. Perez, R., and Walters, R. (2005, January 10–13). An Implicit Compact Polynomial Chaos Formulation for the Euler Equations. Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA. AIAA 2005-1406.10.2514/6.2005-1406 ↗
28. Chaospy: An open source tool for designing methods of uncertainty quantification10.1016/j.jocs.2015.08.008 ↗
29. (2009, September 29). NISP Details. Available online: http://atoms.scilab.org/toolboxes/NISP/2.1.
30. Progress in turbulence/transition modeling
31. Zarmehri, A. (2012). CFD with OpenSource Software: γ − Rθ Transitional Turbulence Model Tutorial, Chalmers University of Technology.
32. Detached eddy simulation of flow around A-airfoil10.1023/B:APPL.0000014933.66058.22 ↗
33. Hallback, M. (1996). One-Point Closures Applied to Transition. Turbulence and Transition Modeling, Kluwer.10.1007/978-94-015-8666-5 ↗
34. Rumsey, C.L. (2009, February 13). Turbulence Modeling Resource, Available online: http://turbmodels.larc.nasa.gov/.
35. Numerical simulations of turbulent flow over airfoils near and during static stall10.2514/1.C034186 ↗
36. The R-γ transition prediction model10.1080/10618562.2014.1002485 ↗