We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a system of nonlinear differential algebraic equations (DAEs). With our modeling approach, we reduce the number of algebraic constraints, which correspond to the $ (2,2) $ block in our semi-explicit DAE model, to the order of junction nodes in the network, where a junction node couples at least three pipelines. We can furthermore ensure that the $ (1, 1) $ block of all system matrices including the Jacobian is block lower triangular by using a specific ordering of the pipes of the network. We then exploit this structure to propose an efficient preconditioner for the fast simulation of the network. We test our numerical methods on benchmark problems of (well-)known gas networks and the numerical results show the efficiency of our methods.

中文翻译：

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燃气网络建模和仿真的高效数值方法

我们研究天然气管道网络的建模和仿真，重点是瞬态动力学仿真的快速数值方法。所获得的基础网络的数学模型由非线性微分代数方程组（DAE）表示。通过我们的建模方法，我们将代数约束的数量减少到网络中结点的顺序，该数量对应于半显式DAE模型中的$（2,2）$块，其中结点至少耦合三个管道。我们还可以通过使用网络管道的特定顺序，确保包括雅可比行列在内的所有系统矩阵的$（1，1）$块为下三角块。然后，我们利用此结构为网络的快速仿真提出有效的预处理器。