{
  "id": "1705.09350",
  "version": "v1",
  "published": "2017-05-25T20:23:57.000Z",
  "updated": "2017-05-25T20:23:57.000Z",
  "title": "An efficient algorithm for simulating ensembles of parameterized flow problems",
  "authors": [
    "Max Gunzburger",
    "Nan Jiang",
    "Zhu Wang"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the individually independent members of the set are subject to different viscosity coefficients, initial conditions, and/or body forces. The proposed scheme applied to the flow ensemble leads to need to solve a single linear system with multiple right-hand sides, and thus is computationally more efficient than solving for all the simulations separately. We show that the scheme is nonlinearly and long-term stable under certain conditions on the time-step size and a parameter deviation ratio. Rigorous numerical error estimate shows the scheme is of first-order accuracy in time and optimally accurate in space. Several numerical experiments are presented to illustrate the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-25T20:23:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parameterized flow problems",
      "efficient algorithm",
      "simulating ensembles",
      "parameter deviation ratio",
      "multiple right-hand sides"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}