{
  "id": "2208.11949",
  "version": "v1",
  "published": "2022-08-25T09:09:05.000Z",
  "updated": "2022-08-25T09:09:05.000Z",
  "title": "Finite element methods for multicomponent convection-diffusion",
  "authors": [
    "Francis R. A. Aznaran",
    "Patrick E. Farrell",
    "Charles W. Monroe",
    "Alexander J. Van-Brunt"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "physics.flu-dyn"
  ],
  "abstract": "We develop finite element methods for coupling the steady-state Onsager-Stefan-Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Employing a novel variational formulation for general non-ideal fluids, we prove well-posedness of a Picard-type linearization, and convergence of its discretization with appropriate finite elements. The application of the method to non-ideal fluids is illustrated with a simulation of the microfluidic mixing of hydrocarbons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-25T09:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "80M10",
      "65N30",
      "76T30"
    ],
    "keywords": [
      "finite element methods",
      "multicomponent convection-diffusion",
      "steady-state onsager-stefan-maxwell equations",
      "low reynolds number",
      "common thermodynamic phase"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}