{
  "id": "2302.04433",
  "version": "v1",
  "published": "2023-02-09T04:41:13.000Z",
  "updated": "2023-02-09T04:41:13.000Z",
  "title": "Efficient numerical methods for the Navier-Stokes-Nernst-Planck-Poisson equations",
  "authors": [
    "Xiaolan Zhou",
    "Chuanju Xu"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated treatment of the terms coupling different equations. By introducing a dynamic equation for the auxiliary variable and reformulating the original equations into an equivalent system, we construct first- and second-order semi-implicit linearized schemes for the underlying problem. The main advantages of the proposed method are: (1) the schemes are unconditionally stable in the sense that a discrete energy keeps decay during the time stepping; (2) the concentration components of the discrete solution preserve positivity and mass conservation; (3) the delicate implementation shows that the proposed schemes can be very efficiently realized, with computational complexity close to a semi-implicit scheme. Some numerical examples are presented to demonstrate the accuracy and performance of the proposed method. As far as the best we know, this is the first second-order method which satisfies all the above properties for the Navier-Stokes-Nernst-Planck-Poisson equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-09T04:41:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "efficient numerical methods",
      "paper efficient first/second-order time-stepping schemes",
      "discrete energy keeps decay",
      "discrete solution preserve positivity",
      "evolutional navier-stokes-nernst-planck-poisson equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}