{
  "id": "1807.07142",
  "version": "v1",
  "published": "2018-07-18T20:53:14.000Z",
  "updated": "2018-07-18T20:53:14.000Z",
  "title": "Efficient Numerical Methods for Gas Network Modeling and Simulation",
  "authors": [
    "Yue Qiu",
    "Sara Grundel",
    "Martin Stoll",
    "Peter Benner"
  ],
  "comment": "25 pages, 21 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "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 nonlinear differential algebraic equation (DAE). By introducing the concept of \\textit{long pipes}, we can reduce the dimension of the algebraic constraints in the resulting DAEs. We introduce a so-called \\textit{flow direction following} (FDF) ordering technique to order the \\textit{long pipes} of the network, and we obtain a block lower-triangular matrix structure of the $(1, 1)$ block for the system matrix of the DAE model. We further exploit such a matrix structure in the DAE model and 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 advantage of our methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T20:53:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "efficient numerical methods",
      "gas network modeling",
      "simulation",
      "block lower-triangular matrix structure",
      "nonlinear differential algebraic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}