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We develop a weakly intrusive framework to simulate the propagation ofuncertainty in solutions of generic hyperbolic partial differential equationsystems on graph-connected domains with nodal coupling and boundary conditions.The method is based on the Stochastic Finite Volume (SFV) approach, and can beapplied for uncertainty quantification (UQ) of the dynamical state of fluidflow over actuated transport networks. The numerical scheme has specificadvantages for modeling intertemporal uncertainty in time-varying boundaryparameters, which cannot be characterized by strict upper and lower (interval)bounds. We describe the scheme for a single pipe, and then formulate thecontrolled junction Riemann problem (JRP) that enables the extension to generalnetwork structures. We demonstrate the method's capabilities and performancecharacteristics using a standard benchmark test network.

Stochastic Finite Volume Method for Uncertainty Quantification of Transient Flow in Gas Pipeline Networks