Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks.

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach, and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. We demonstrate the method's capabilities and performance characteristics using a standard benchmark test network. • Formulation of a stochastic hyperbolic PDE as a high-dimensional parametric PDE. • Novel SFV method for quantification of intertemporal uncertainty in systems of conservation laws posed on graphs. • Formulation of the stochastic junction Riemann problem to compute numerical fluxes at the nodes of the graph. • Application of the SFV method to a real-world problem of stochastic gas flows on networks. • Convergence analysis for the statistical moments of the solution. [ABSTRACT FROM AUTHOR]