{
  "id": "1905.09023",
  "version": "v1",
  "published": "2019-05-22T08:52:24.000Z",
  "updated": "2019-05-22T08:52:24.000Z",
  "title": "A bi-fidelity method for the multiscale Boltzmann equation with random parameters",
  "authors": [
    "Liu Liu",
    "Xueyu Zhu"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C. Gittelson and D. Xiu, SIAM J. Sci. Comput., 36 (2014); X. Zhu, A. Narayan and D. Xiu, SIAM J. Uncertain. Quantif., 2 (2014)]. By choosing the compressible Euler system as the low-fidelity model, we adapt the bi-fidelity SC method to combine computational efficiency of the low-fidelity model with high accuracy of the high-fidelity (Boltzmann) model. With only a small number of high-fidelity asymptotic-preserving solver runs for the Boltzmann equation, the bi-fidelity approximation can capture well the macroscopic quantities of the solution to the Boltzmann equation in the random space. A priori estimate on the accuracy between the high- and bi-fidelity solutions together with a convergence analysis is established. Finally, we present extensive numerical experiments to verify the efficiency and accuracy of our proposed method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-22T08:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q20",
      "76P05"
    ],
    "keywords": [
      "multiscale boltzmann equation",
      "bi-fidelity method",
      "low-fidelity model",
      "multi-dimensional random parameters",
      "bi-fidelity sc method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}