{
  "id": "2009.11376",
  "version": "v1",
  "published": "2020-09-23T20:58:10.000Z",
  "updated": "2020-09-23T20:58:10.000Z",
  "title": "A Positive and Stable L2-minimization Based Moment Method for the Boltzmann Equation of Gas dynamics",
  "authors": [
    "Neeraj Sarna"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider the method-of-moments approach to solve the Boltzmann equation of rarefied gas dynamics, which results in the following moment-closure problem. Given a set of moments, find the underlying probability density function. The moment-closure problem has infinitely many solutions and requires an additional optimality criterion to single-out a unique solution. Motivated from a discontinuous Galerkin velocity discretization, we consider an optimality criterion based upon L2-minimization. To ensure a positive solution to the moment-closure problem, we enforce positivity constraints on L2-minimization. This results in a quadratic optimization problem with moments and positivity constraints. We show that a (Courant-Friedrichs-Lewy) CFL-type condition ensures both the feasibility of the optimization problem and the L2-stability of the moment approximation. Numerical experiments showcase the accuracy of our moment method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-23T20:58:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boltzmann equation",
      "moment method",
      "gas dynamics",
      "stable l2-minimization",
      "moment-closure problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}