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
Journal of Computational Physics
Uncertainty quantification in hybrid dynamical systems
Journal of Computational Physics
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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.