Uncertainty quantification in kinematic-wave models

Authors:
Peng Wang;Daniel M. Tartakovsky
Affiliations:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA;Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA
Venue:
Journal of Computational Physics
Year:
2012

Citing 2
Cited 1

Predicting shock dynamics in the presence of uncertainties

Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems

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Uncertainty quantification in hybrid dynamical systems

Journal of Computational Physics

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Abstract

We develop a probabilistic approach to quantify parametric uncertainty in first-order hyperbolic conservation laws (kinematic wave equations). The approach relies on the derivation of a deterministic equation for the cumulative density function (CDF) of a system state, in which probabilistic descriptions (probability density functions or PDFs) of system parameters and/or initial and boundary conditions serve as inputs. In contrast to PDF equations, which are often used in other contexts, CDF equations allow for straightforward and unambiguous determination of boundary conditions with respect to sample variables. The accuracy and robustness of solutions of the CDF equation for one such system, the Saint-Venant equations of river flows, are investigated via comparison with Monte Carlo simulations.