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.

翻译：我们提出一种预测-校正自适应方法，用于模拟网络上的双曲型偏微分方程（PDE），该方程考虑了参数、初始条件或边界条件中的一般不确定性。该方法基于随机有限体积（SFV）框架，无需采样方案或模拟集合，同时保持基本性质，特别是所得系统的双曲性和离散解的守恒性。在代表管道的网络连接一维域集合上，初始边界值问题（IBVP）采用物理空间和随机空间的主动离散化表示，并通过求解连接点黎曼问题来评估不确定性在网络节点间的传播。该方法基于误差指标进行离散化细化的自适应性，能够以计算上可行的方式评估跨期不确定性，从而支持在瞬态和不确定条件下优化管道运行时机和输量的决策，以最大化输送效率。我们通过代表性网络的仿真展示了该计算方法。