{
  "annotation_id": "84809eae-6a73-44d9-bf7f-6eb27e971837",
  "date_created": "2026-03-02T18:00:39.034000Z",
  "date_modified": "2026-03-02T18:00:39.034000Z",
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  "record": {
    "abstract": "An improved numerical solver for the unified solution of compressible and\nincompressible fluids involving interfaces is proposed. The present method is\nbased on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified\nProcedure) method, which is a pressure-based semi-implicit solver for the Euler\nequations of fluid flows. In Part I of this series of articles [M. Ida, Comput.\nPhys. Commun. 132 (2000) 44], we proposed an improved scheme for the convection\nterms in the equations, which allowed us discontinuous descriptions of the\ndensity interface by replacing the cubic interpolation function used in the CIP\nscheme with a quadratic extrapolation function only around the interface. In\nthis paper, as Part II of this series, the multi-time-step integration\ntechnique is adapted to the CIP-CUP integration. Because the CIP-CUP treats\ndifferent-nature components in the fluid equations separately, the adaptation\nof the technique is straightforward. This modification allows us flexible\ndeterminations of the time interval, which results in an efficient and accurate\nintegration. Furthermore, some additional discussion on our methods is\npresented. Finally, the application results to composite flow problems such as\ncompressible and incompressible Kelvin-Helmholtz instabilities and the dynamics\nof two acoustically coupled deformable bubbles in a viscous liquid are\nprovided.",
    "arxiv_id": "physics/0203074",
    "authors": [
      "Masato Ida"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.flu-dyn"
    ],
    "doi": "10.1016/S0010-4655(02)00691-4",
    "journal_ref": "Comput. Phys. Commun. 150 (3) pp.300-323 (2003)",
    "title": "An improved unified solver for compressible and incompressible fluids   involving free surfaces. II. Multi-time-step integration and applications",
    "url": "https://arxiv.org/abs/physics/0203074"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "895ca8d4-44b4-4809-8fa4-73fe38e2a80e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}