Abstract In previous papers, the authors introduced a new formulation of the flow equations, involving friction and gravity effects, in gas transportation networks. They also proposed finite element methods combined with Newton-like algorithms for numerical solution. The main goal of the present paper is to include into the above formulation the usual devices existing in a gas transmission network other than pipelines, namely, compressors, pressure control valves (PCV), flow control valves (FCV) and resistors. One of the main novelties of this paper is that, unlike many related ones, all of the above devices are modelled as nodes instead of edges of the graph which makes numerical solution simpler and computationally cheaper. This is the case, for instance, in the frequent situation where there are many valves in the network but only a few of them are working in each specific simulation scenario. Instead of introducing one edge per valve in the graph, we only consider that, at specific time intervals, some valves are acting which leads to simple modifications in the discrete system which are made dynamically and locally. An interesting feature of the full discrete model is that mass conservation is exactly preserved which is a very important issue, particularly for long time simulations.

中文翻译：

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在输气管网的有限元仿真中对压缩机、电阻器和阀门进行建模

摘要 在之前的论文中，作者介绍了一种新的流动方程公式，涉及气体运输网络中的摩擦和重力效应。他们还提出了结合牛顿类算法的有限元方法进行数值求解。本文的主要目标是将气体传输网络中除管道外的常见设备包括在上述公式中，即压缩机、压力控制阀 (PCV)、流量控制阀 (FCV) 和电阻器。本文的主要新颖之处之一是，与许多相关设备不同，所有上述设备都被建模为节点而不是图的边，这使得数值求解更简单，计算成本更低。这种情况，例如，在网络中有许多阀门但只有少数阀门在每个特定模拟场景中工作的常见情况下。不是在图中为每个阀门引入一条边，我们只考虑在特定的时间间隔内，一些阀门在起作用，这导致离散系统中的动态和局部进行简单修改。完全离散模型的一个有趣特征是质量守恒被精确保留，这是一个非常重要的问题，特别是对于长时间模拟。