Uncertainty quantification in kinematic-wave models

Journal of Computational Physics

Volumn 231, Issue 23, 2012, Pages 7868-7880

  Wang, Peng ^a,b   Tartakovsky, Daniel M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

Author keywords

Hyperbolic conservation law; Probability density function; Random parameters; Uncertainty quantification

Indexed keywords

HYPERBOLIC FUNCTIONS; INTELLIGENT SYSTEMS; KINEMATICS; MONTE CARLO METHODS; PHYSICAL PROPERTIES; PROBABILITY DENSITY FUNCTION; UNCERTAINTY ANALYSIS; WAVE EQUATIONS;

CUMULATIVE DENSITY FUNCTIONS; FIRST ORDER; FUNCTION EQUATIONS; HYPERBOLIC CONSERVATION LAWS; KINEMATIC WAVE EQUATION; KINEMATIC WAVE MODELS; PARAMETRIC UNCERTAINTIES; PROBABILISTICS APPROACH; RANDOM PARAMETERS; UNCERTAINTY QUANTIFICATIONS;

BOUNDARY CONDITIONS;

EID: 84866035685     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.07.030     Document Type: Article

References (30)

1. Lighthill M.J., Whitham G.B. On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. London Ser. A 1955, 229(1178):281-316.
2. Lighthill M.J., Whitham G.B. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. London Ser. A 1955, 229(1178):317-345.
3. Singh V.P. Kinematic Wave Modeling in Water Resources: Surface Water Hydrology 1996, Wiley, New York.
4. Singh V.P. Kinematic wave modeling in water resources: a historical perspective. Hydrol. Process. 2001, 15:671-706.
5. Moore R.J., Cole S.J., Bell V.A., Jones D.A. Issues in flood forecasting: ungauged basins, extreme floods and uncertainty. International Association of Hydrological Sciences 2006, vol. 305:103-122. IAHS Publ. I. Tchiguirinskaia, K.N.N. Thein, P. Hubert (Eds.).
6. Eagleson P.S. Dynamics of flood frequency. Water Resour. Res. 1972, 8(4):878-898.
7. Kavvas M., Govindaraju R.S. Stochastic overland flows, part 1: Physics-based evolutionary probability distributions. Stoch. Hydrol. Hydraul. 1991, 5(2):89-104.
8. Govindaraju R.S., Kavvas M. Stochastic overland flows, part 2: Numerical solutions evolutionary probability density functions. Stoch. Hydrol. Hydraul. 1991, 5(2):105-124.
9. Kavvas M. Nonlinear hydrologic processes: conservation equations for determining their means and probability distributions. J. Hydrol. Eng. 2003, 8(2):44-53.
10. Yoon J., Kavvas M.L. Probabilistic solution to stochastic overland flow equation. J. Hydrol. Eng. 2003, 8(2):54-63.
11. Séguis L., Cappelaere B., Peugeot C., Vieux B. Impact on Sahelian runoff of stochastic and elevation-induced spatial distributions of soil parameters. Hydrol. Process. 2002, 16(2):313-332.
12. Morbidelli R., Corradini C., Govindaraju R.S. A simplified model for estimating field-scale surface runoff hydrographs. Hydrol. Process. 2007, 21(13):1772-1779.
13. Lin G., Su C.-H., Karniadakis G.E. Predicting shock dynamics in the presence of uncertainties. J. Comput. Phys. 2006, 217(1):260V276.
14. R. Abgrall, A simple, flexible and generic deterministic approach to uncertainty quantifications in non linear problems: application to fluid flow problems, Tech. rep., Rapport de Recherche INRIA, 2007.
15. Tryoen J., Le Mai{dotless}̌tre O., Ndjing M., Ern A. Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. J. Comput. Phys. 2010, 229(18):6485-6511.
16. Abgrall R., Congedo P.M., Corre C., Galéra S. A simple semi-intrusive method for uncertainty quantification of shocked flows, comparison with a non-intrusive polynomial chaos method. V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010 2010, Lisbon, Portugal, ISBN: 978-989-96778-1-4. J.C.F. Pereira, A. Sequeira, J.M.C. Pereira (Eds.).
17. Ge L., Cheung K.F. Spectral sampling method for uncertainty propagation in long-wave runup modeling. J. Hydraul. Eng. 2011, 137(3):277-288.
18. Poëtte G., Després B., Lucor D. Uncertainty propagation for systems of conservation laws, high order stochastic spectral methods. Lecture Notes in Computational Science and Engineering 2011, vol. 76:293-305. Springer-Verlag, Berlin Heidelberg. J.S. Hesthaven, E.M. Rnquist (Eds.).
19. Pope S.B. Turbulent Flows 2000, Cambridge University Press.
20. Tartakovsky D.M., Broyda S. PDF equations for advective-reactive transport in heterogeneous porous media with uncertain properties. J. Contam. Hydrol. 2011, 120-121:129-140.
21. Seddon J.A. River hydraulics. Trans. Amer. Soc. Civ. Eng. 1900, 43:179-243.
22. Buhman D.L., Gates T.K., Watson C.C. Stochastic variability of fluvial hydraulic geometry: mississippi and red rivers. J. Hydrol. Eng. 2002, 128:426-437.
23. Gates T.K., Al-Zahrani M. Spatiotemporal stochastic open-channel flow. I: Model and its parameter data. J. Hydrol. Eng. 1996, 122(11):641-651.
24. Gates T.K., Al-Zahrani M. Spatiotemporal stochastic open-channel flow. II: Simulation experiments. J. Hydrol. Eng. 1996, 122(11):652-661.
25. Moramarco T., Singh V.P. A practical method for analysis of river waves and for kinematic wave routing in natural channel networks. Hydrol. Process. 2000, 14:51-62.
26. Gottlieb D., Xiu D. Galerkin method for wave equations with uncertain coefficients. Commun. Comput. Phys. 2008, 3(2):505-518.
27. Kraichnan R.H. Eddy viscosity and diffusivity: exact formulas and approximations. Complex Syst. 1987, 1:805-820.
28. Tartakovsky D.M., Guadagnini A., Ballio F., Tartakovsky A.M. Localization of mean flow and equivalent transmissivity tensor for bounded randomly heterogeneous aquifers. Transp. Porous Media 2002, 49(1):41-58.
29. Ditlevsen O., Mohr G., Hoffmeyer P. Integration of non-Gaussian fields. Probab. Eng. Mech. 1996, 11:15-23.
30. Liang L., Kavvas M.L. Modeling of solute transport and macrodispersion by unsteady stream flow under uncertain conditions. J. Hydrol. Eng. 2008, 13(6):510-520.