论文标题
大型网络中不确定气体传输的自适应单级随机搭配方法
Adaptive Single- and Multilevel Stochastic Collocation Methods for Uncertain Gas Transport in Large-Scale Networks
论文作者
论文摘要
在本文中，我们关注的是对通过大规模网络运输的天然气的日期振荡产生的不确定性的量化。气流的短期瞬态动力学是由基于等激素Euler方程的平衡法的双曲线系统的层次结构建模的。我们扩展了一种新型的自适应策略，用于通过Lang，Scheichl和Silvester最近提出和分析的随机数据求解椭圆PDE [J。计算。 Phys。，419：109692，2020]，为了不确定的气体传输问题。样品依赖性的自适应网格和物理空间中的模型改进与随机空间中的自适应各向异性稀疏Smolyak网格结合使用。一种单级方法可以平衡物理和随机近似的离散误差以及多级方法，该方法还考虑了将计算成本降至最低的多级方法。来自公共天然气库的两个示例表明，从随机数量的关注数量计算出的期望的误差控制的可靠性，以及随机插值的进一步使用，例如，在网络出口处，最小压力值和最大压力值的近似概率密度函数。
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.
