{
  "id": "2106.07154",
  "version": "v1",
  "published": "2021-06-14T04:20:57.000Z",
  "updated": "2021-06-14T04:20:57.000Z",
  "title": "Local time stepping for the shallow water equations in MPAS-Ocean",
  "authors": [
    "Giacomo Capodaglio",
    "Mark Petersen"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We assess the performance of a set of local time-stepping schemes for the shallow water equations implemented in the global ocean model MPAS-Ocean. The availability of local time-stepping tools is of major relevance for ocean codes such as MPAS-Ocean, which rely on a multi-resolution approach to perform regional grid refinement, for instance in proximity of the coast. In presence of variable resolution, the size of the time-step of explicit numerical integrators is bounded above by the size of the smallest cell on the grid, according to the Courant-Friedrichs-Lewy (CFL) condition. This constraint means that the time-step size used in low resolution regions must be the same as the one used in high resolution regions, resulting in an unnecessary computational effort. Local time-stepping, on the other hand, allows one to select different time-step sizes according to local, rather than global, CFL conditions, resulting in a more tailored integration process and reduced computational times. The present work is a preliminary but necessary effort aimed at paving the way for a more comprehensive work on local time-stepping for the primitive equation set with realistic geography.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-14T04:20:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shallow water equations",
      "local time stepping",
      "local time-stepping",
      "perform regional grid refinement",
      "global ocean model mpas-ocean"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}