Backward uncertainty propagation method in flow problems: Application to the prediction of rarefaction shock waves

Computer Methods in Applied Mechanics and Engineering

Volumn 213-216, Issue , 2012, Pages 314-326

  Congedo, P M ^a   Colonna, P ^b   Corre, C ^c   Witteveen, J A S ^d   Iaccarino, G ^d  

^a INRIA   (France)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c VERIMAG   (France)

^d Stanford University   (United States)

Author keywords

Dense gas shock tube; Inverse analysis; Polynomial chaos; Rarefaction shock wave; Uncertainty quantification

Indexed keywords

EFFICIENT ALGORITHM; FLOW PROBLEMS; HIGHLY SENSITIVE; INITIAL FLOW; INVERSE ANALYSIS; NUMERICAL STUDIES; POLYNOMIAL CHAOS; PROBABILITY OF OCCURRENCE; RELIABLE ESTIMATES; REPRODUCIBILITIES; THERMODYNAMIC MODEL; UNCERTAINTY PROPAGATION; UNCERTAINTY QUANTIFICATIONS;

ALGORITHMS; COMPUTATIONAL FLUID DYNAMICS; SHOCK TUBES; TUBES (COMPONENTS);

UNCERTAINTY ANALYSIS;

EID: 84856084092     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.12.009     Document Type: Article

References (41)

1. H.A. Bethe, The theory of shock waves for an arbitrary equation of state, Technical report No. 545, Office of Scientific Research and Development, 1942.
2. Zel'dovich Y.B. On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 1946, 4:363.
3. Thompson P.A. A fundamental derivative in gas dynamics. Phys. Fluids 1971, 14(2):1843-1853.
4. Colonna P., Guardone A., Nannan N.R., der Stelt T.P.V. On the computation of the fundamental derivative of gas dynamics using equations of state. Fluid Phase Equilibr. 2009, 286:43-54.
5. Colonna P., Guardone A., Nannan N.R., Zamfirescu C. Design of the dense gas flexible asymmetric shock tube. J. Fluid Engrg. Trans. ASME 2008, 130(034501):1-6.
6. Brown B.P., Argrow B.M. Application of Bethe-Zel'dovic-Thompson fluids in organic Rankine cycle engines. J. Power Sources 2000, 16:1118.
7. Monaco J.F., Cramer M.S., Watson L.T. Supersonic flows of dense gases in cascade configurations. J. Fluid Mech. 1997, 330:375-409.
8. Colonna P., Rebay S. Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver. Int. J. Numer. Methods Fluids 2004, 46(7):735-765.
9. Colonna P., Guardone A. Molecular interpretation of nonclassical gas dynamics of dense vapors under the van der Waals model. Phys. Fluids 2006, 056101:1-14.
10. Zamfirescu C., Guardone A., Colonna P. Admissibility region for rarefaction shock waves in dense gases. J. Fluid Mech. 2008, 599:363-381.
11. Colonna P., Silva P. Dense gas thermodynamic properties of single and multi-component fluids for fluid dynamics simulations. J. Fluid Engrg. Trans. ASME 2003, 125(3):414-427.
12. Colonna P., Nannan N.R., Guardone A., Lemmon E.W. Multiparameter equations of state for selected siloxanes. Fluid Phase Equilibr. 2006, 244:193-211.
13. Nannan N.R., Colonna P., Tracy C.M., Rowley R.L., Hurky J.J. Ideal-gas heat capacities of dimethylsiloxanes from speed-of-sound measurements and ab initio calculations. Fluid Phase Equilibr. 2007, 257:102-113.
14. Colonna P., Nannan N.R., Guardone A. Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i=1,...,3, and [O-Si-(CH3)2]6. Fluid Phase Equilibr. 2008, 263(2):115-130.
15. Colonna P., Guardone A., Nannan N.R. Siloxanes: a new class of candidate Bethe-Zel'dovich-Thompson fluids. Phys. Fluids 2006, 19(8):1-12.
16. Guardone A., Zamfirescu C., Colonna P. Maximum intensity of rarefaction shock waves for dense gases. J. Fluid Mech. 2010, 642:127-146.
17. Cinnella P., Congedo P.M., Pediroda V., Parussini L. Quantification of thermodynamic uncertainties in real gas flows. Int. J. Engrg. Syst. Model. Simul. 2010, 2(1-2):12-24.
18. Desceliers C., Ghanem R., Soize C. Maximum likelihood estimation of stochastic chaos representations from experimental data. Int. J. Numer. Methods Engrg. 2006, 66:978-1001.
19. Ma X., Zabaras N. An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method. Inverse Probl. 2009, 25:035013.
20. Asokan V., Zabaras N. Stochastic inverse heat conduction using a spectral approach. Int. J. Numer. Methods Engrg. 2004, 60:1569-1593.
21. Zabaras N., Ganapathysubramanian B. A scalable framework for the solution of stochastic inverse problem using a sparse grid collocation approach. J. Comput. Phys. 2008, 227:4697-4735.
22. Ngnepieba P., Hussaini M. An efficient sampling method for stochastic inverse problems. Comput. Optim. Appl. 2007, 37:121-138.
23. A. Abusam, K. Keesman, G. van Straten, Forward and backward probabilistic simulations in Geotechnical engineering, in: Contemporary Topics in In Situ Testing, Analysis, and Reliability of Foundations (GSP 186), vol. 186, 2009, pp. 332-339.
24. Ait-Sahalia Y., Kimmel R. Maximum likelihood estimation of stochastic volatility models. J. Financ. Econ. 2007, 83:413-452.
25. Abusam A., Keesman K., van Straten G. Forward and backward uncertainty propagation: an oxidation ditch modelling example. Water Res. 2003, 37:429-435.
26. Colonna P., Rebay S., Harinck J., Guardone A. Real-gas effects in organic Rankine cycle turbine nozzles. J. Propul. Power 2008, 24:282-294.
27. Harinck J., Colonna P., Guardone A. The influence of molecular complexity on expanding flows of ideal and dense gases. J. Fluid Mech. 2009, 21(8):086101-1-086101-14.
28. Harinck J., Colonna P., Guardone A., Rebay S. Influence of thermodynamic models in 2D flow simulations of turboexpanders. J. Turbomach. 2010, 132:11001-110017.
29. S. Rebay, P. Colonna, D. Pasquale, A. Ghidoni, Simulation of the turbulent dense gas flow through the nozzle of an organic Rankine cycle turbine, in: Proceedings of the 8th European Turbomachinery Conference, 2009, pp. 1137-1148.
30. Turunen-Saaresti T., Harinck J., Colonna P., van Buijtenen J. Computational study of a high-expansion ratio radial ORC turbine stator. J. Engrg. Gas Turb. Power. 2010, 132:11001-110017.
31. Colonna P., van der Stelt T. FluidProp: A Program for the Estimation of Thermophysical Properties of Fluids 2005, Energy Technology Section, Delft University of Technology, The Netherlands.
32. Congedo P.M., Corre C., Cinnella P. Airfoil shape optimization for transonic flows of Bethe-Zel'dovich-Thompson fluids. AIAA J. 2007, 45(6):1303-1316.
33. Congedo P.M., Corre C., Martinez J.-M. Shape optimization of an airfoil in a BZT flow with multiple-source uncertainties. Comput. Methods Appl. Mech. Engrg. 2011, 200(1):216-232.
34. Cinnella P. Roe-type schemes for dense gas flow computations. Comput. Fluids 2006, 35(10):1264-1281.
35. Stryjek R., Vera J.H. PRSV: an improved Peng-Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Engrg. 1986, 64:323-333.
36. J.A.S. Witteveen, G. Iaccarino, Simplex elements stochastic collocation in higher-dimensional probability spaces, in: 12th AIAA Non-Deterministic Approaches Conference, Orlando, Florida, AIAA 2010-2924.
37. Ghanem R.G., Spanos S.D. Stochastic Finite Elements: A Spectral Approach 1991, Springer-Verlag.
38. Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. J. Sci. Comput. 2002, 26:1-10.
39. Cameron R.H., Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 1947, 48(1):385.
40. Cinnella P., Congedo P.M. Optimal airfoil shapes for viscous transonic flows of Bethe-Zel'dovich-Thompson fluids. Comput. Fluids 2008, 37:250-264.
41. Gao Z., Hesthaven J. Efficient solution of ordinary differential equations with high-dimensional parametrized uncertainty. Commun. Comput. Phys. 2011, 10:253-278.