Adaptive Single- and Multilevel Stochastic Collocation Methods for Uncertain Gas Transport in Large-Scale Networks

TL;DR

This paper develops adaptive single- and multilevel stochastic collocation methods to quantify uncertainties in gas transport through large-scale networks, improving accuracy and efficiency in modeling transient dynamics with random demand fluctuations.

Contribution

It extends adaptive strategies for elliptic PDEs to uncertain gas transport problems, combining adaptive meshes and sparse grids for better error control and cost reduction.

Findings

Reliable error control of expectations for random gas quantities

Effective approximation of probability density functions of pressure extremes

Demonstrated efficiency on real-world gas network examples

Abstract

In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is modelled by a hierarchy of hyperbolic systems of balance laws based on the isentropic Euler equations. We extend a novel adaptive strategy for solving elliptic PDEs with random data, recently proposed and analysed by Lang, Scheichl, and Silvester [J. Comput. Phys., 419:109692, 2020], to uncertain gas transport problems. Sample-dependent adaptive meshes and a model refinement in the physical space is combined with adaptive anisotropic sparse Smolyak grids in the stochastic space. A single-level approach which balances the discretization errors of the physical and stochastic approximations and a multilevel approach which additionally minimizes the computational costs are considered. Two examples taken from a public gas library demonstrate the reliability of the error control of expectations calculated from random quantities of interest, and the further use of stochastic interpolants to, e.g., approximate probability density functions of minimum and maximum pressure values at the exits of the network.