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