Stochastic Active Discretizations for Accelerating Temporal Uncertainty Management of Gas Pipeline Loads

Abstract: We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based on the stochastic finite volume (SFV) framework that circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. The initial boundary value problem (IBVP) on a set of network-connected one-dimensional domains that represent a pipeline is represented using active discretization of the physical and stochastic spaces, and we evaluate the propagation of uncertainty through network nodes by solving a junction Riemann problem. The adaptivity of our method in refining discretization based on error metrics enables computationally tractable evaluation of intertemporal uncertainty in order to support decisions about timing and quantity of pipeline operations to maximize delivery under transient and uncertain conditions. We illustrate our computational method using simulations for a representative network.