Efficient computation of unsteady flow in complex river systems with uncertain inputs

References

• I. Babuška, K.M. Liu, and R. Tempone, Solving stochastic partial differential equations based on the experimental data, Math. Models Methods Appl. Sci. 13 (2003), pp. 415–444, dedicated to Jim Douglas, Jr. on the occasion of his 75th birthday.
   Google Scholar
• I. Babuška, F. Nobile, and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal. 45 (2007. ), pp. 1005–1034 doi: 10.1137/050645142
   Web of Science ®Google Scholar
• M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: A non intrusive approach by regression, Eur. J. Comput. Mech. 15 (2006), pp. 81–92.
   Google Scholar
• G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, J. Comput. Phys. 230 (2011), pp. 2345–2367. doi: 10.1016/j.jcp.2010.12.021
   Web of Science ®Google Scholar
• Q. Chen, D. Gottlieb, and J. Hesthaven, Uncertainty analysis for the steady-state flows in a dual throat nozzle, J. Comput. Phys. 204 (2005), pp. 378–398. doi: 10.1016/j.jcp.2004.10.019
   Web of Science ®Google Scholar
• P.G. Constantine, A. Doostan, and G. Iaccarino, A hybrid collocation/Galerkin scheme for convective heat transfer problems with stochastic boundary conditions, Internat. J. Numer. Methods Engrg. 80 (2009), pp. 868–880. doi: 10.1002/nme.2564
   Web of Science ®Google Scholar
• P.G. Constantine, M.S. Eldred, and E.T. Phipps, Sparse pseudospectral approximation method, Comput. Methods Appl. Mech. Engrg. 229 (2012), pp. 1–12. doi: 10.1016/j.cma.2012.03.019
   Web of Science ®Google Scholar
• T. Gerstner and M. Griebel, Dimension–adaptive tensor–product quadrature, Computing 71 (2003), pp. 65–87. doi: 10.1007/s00607-003-0015-5
   Web of Science ®Google Scholar
• R.G. Ghanem and A. Doostan, On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data, J. Comput. Phys. 217 (2006), pp. 63–81. doi: 10.1016/j.jcp.2006.01.037
   Web of Science ®Google Scholar
• R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York, 1991.
   Google Scholar
• R.G. Ghanem, S.F. Masri, M.F. Pellissetti, and R. Wolfe, Identification and prediction of stochastic dynamical systems in a polynomial chaos basis, Comput. Methods Appl. Mech. Engrg. 194 (2005), pp. 1641–1654. doi: 10.1016/j.cma.2004.05.031
   Web of Science ®Google Scholar
• N.L. Gibson, L.A. Gomez, A.S. Leon, and V.S. Vasylkivska, Domain decomposition approach for unsteady flow routing utilizing performance graphs, 2013, to be submitted.
   Google Scholar
• N.L. Gibson, M.G. McIntire, C. Hoyle, and V.S. Vasylkivska, Robust reservoir operation with probabilistic constraints, 2013, to be submitted.
   Google Scholar
• M.D. Gunzburger, J.S. Peterson, and H. Kwon, An optimization based domain decomposition method for partial differential equations, Comput. Math. Appl. 37 (1999), pp. 77–93. doi: 10.1016/S0898-1221(99)00127-3
   Web of Science ®Google Scholar
• T.Y. Hou, W. Luo, B. Rozovskii, and H.M. Zhou, Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics, J. Comput. Phys. 216 (2006), pp. 687–706. doi: 10.1016/j.jcp.2006.01.008
   Web of Science ®Google Scholar
• M.A. Hoy and A.R. Schmidt, Unsteady flow routing in sewers using hydraulic and volumetric performance graphs, World Environmental and Water Resource Congress 2006: Examining the Confluence of Environmental and Water Concerns, Omaha, NE, 2006.
   Google Scholar
• O.M. Knio and O.P. Le Maıtre, Uncertainty propagation in CFD using polynomial chaos decomposition, Fluid Dynam. Res. 38 (2006), pp. 616–640. doi: 10.1016/j.fluiddyn.2005.12.003
   Web of Science ®Google Scholar
• A.S. Leon, N.L. Gibson, and C. Gifford-Miears, Toward reduction of uncertainty in complex multi-reservoir river systems, The XIX International Conference on Computational Methods in Water Resources, Urbana, IL, 2012.
   Google Scholar
• A.S. Leon, E.A. Kanashiro, and J.A. González-Castro, A fast approach for unsteady flow routing in complex river networks based on performance graphs, J. Hydraul. Eng. 139 (2013), pp. 284–295. doi: 10.1061/(ASCE)HY.1943-7900.0000678
   Web of Science ®Google Scholar
• Y. Marzouk and D. Xiu, A stochastic collocation approach to Bayesian inference in inverse problems, Commun. Comput. Phys. 6 (2009), pp. 826–847. doi: 10.4208/cicp.2009.v6.p826
   Web of Science ®Google Scholar
• L. Mathelin, M.Y. Hussaini, and T.A. Zang, Stochastic approaches to uncertainty quantification in CFD simulations, Numer. Algorithms 38 (2005), pp. 209–236.
   Web of Science ®Google Scholar
• A. Narayan and D. Xiu, Distributional sensitivity for uncertainty quantification, Commun. Comput. Phys. 10 (2011), pp. 140–160.
   Web of Science ®Google Scholar
• A. Narayan and D. Xiu, Stochastic collocation methods on unstructured grids in high dimensions via interpolation, SIAM J. Sci. Comput. 34 (2012), pp. A1729–A1752.
   Web of Science ®Google Scholar
• B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Saf. 93 (2008), pp. 964–979. doi: 10.1016/j.ress.2007.04.002
   Web of Science ®Google Scholar
• D. Xiu, Efficient collocational approach for parametric uncertainty analysis, Commun. Comput. Phys. 2 (2007), pp. 293–309.
   Web of Science ®Google Scholar
• D. Xiu, Fast numerical methods for stochastic computations: A review, Commun. Comput. Phys. 5 (2009), pp. 242–272.
   Web of Science ®Google Scholar
• D. Xiu, Numerical Methods for Stochastic Computations. A Spectral Method Approach, Princeton University Press, Princeton, NJ, 2010.
   Google Scholar
• D. Xiu and J.S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput. 27 (2005), pp. 1118–1139. doi: 10.1137/040615201
   Web of Science ®Google Scholar
• D. Xiu and G.E. Karniadakis, The Wiener–Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput. 24 (2002), pp. 619–644 (electronic). doi: 10.1137/S1064827501387826
   Web of Science ®Google Scholar
• D. Xiu and S.J. Sherwin, Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network, J. Comput. Phys. 226 (2007), pp. 1385–1407. doi: 10.1016/j.jcp.2007.05.020
   Web of Science ®Google Scholar