{
  "id": "2408.03862",
  "version": "v1",
  "published": "2024-08-07T16:11:30.000Z",
  "updated": "2024-08-07T16:11:30.000Z",
  "title": "A first-order hyperbolic reformulation of the Cahn-Hilliard equation",
  "authors": [
    "Firas Dhaouadi",
    "Michael Dumbser",
    "Sergey Gavrilyuk"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP"
  ],
  "abstract": "In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical Cattaneo-type relaxation that allows to reformulate diffusion equations as augmented first order hyperbolic systems with stiff relaxation source terms. The proposed system is proven to be hyperbolic and to admit a Lyapunov functional, in accordance with the original equations. A new numerical scheme is proposed to solve the original Cahn-Hilliard equations based on conservative semi-implicit finite differences, while the hyperbolic system was numerically solved by means of a classical second order MUSCL-Hancock-type finite volume scheme. The proposed approach is validated through a set of classical benchmarks such as spinodal decomposition, Ostwald ripening and exact stationary solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-07T16:11:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35L65",
      "35L03",
      "65M06",
      "65M08"
    ],
    "keywords": [
      "first-order hyperbolic reformulation",
      "cahn-hilliard equation",
      "first order hyperbolic systems",
      "second order muscl-hancock-type finite",
      "order muscl-hancock-type finite volume scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}