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Solving the Incompressible Navier-Stokes Equations on Oriented Curved Surfaces Discretized by Point Clouds — arXiv:2609.00216

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.00216
License (as archived): CC0-1.0
Archived: 2026-10-17T07:06:06.396Z
SHA-256 of the archived text: 04a058182467c0548f5c7fefdf7ff96147f3bdcd90fc98dafa359fcdde0b567c
Stable URL of this page: https://metraipolis.com/documento/dc_27c1935600f3

How to cite

Solving the Incompressible Navier-Stokes Equations on Oriented Curved Surfaces Discretized by Point Clouds — arXiv:2609.00216 — arXiv (en), https://arxiv.org/abs/2609.00216 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_27c1935600f3 (Metraipolis archive dc_27c1935600f3, sha256 04a058182467c0548f5c7fefdf7ff96147f3bdcd90fc98dafa359fcdde0b567c)

BibTeX

@misc{dc27c1935600f3,
  title = {Solving the Incompressible Navier-Stokes Equations on Oriented Curved Surfaces Discretized by Point Clouds — arXiv:2609.00216},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.00216},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_27c1935600f3; sha256 04a058182467c0548f5c7fefdf7ff96147f3bdcd90fc98dafa359fcdde0b567c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.00216. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We present a meshfree numerical solver for the incompressible Navier-Stokes equations on oriented curved surfaces that are represented by surface point clouds. On curved surfaces, numerical challenges pertaining to stiffness and pressure-velocity coupling are exacerbated. Moreover, vector calculus on curved surfaces differs from its Euclidean counterpart. The presented method operates on surface point clouds in an Eulerian frame of reference without requiring a computational grid or mesh. It achieves consistent approximation in space and time with high order of accuracy; we demonstrate up to order six. The incompressibility constraint is locally imposed as a weak artificial compressibility approximation, avoiding global matrix inversion. We show that the method provides consistent and convergent approximations of surface vector fields and differential operators. We study the relationship between error, spatial resolution, and artificial Mach number and characterize the frequency spectrum of the artificial oscillations. We provide numerical solutions of the incompressible Navier-Stokes equations on symmetric surfaces, such as the sphere and torus, and on parametric and non-parametric asymmetric surfaces. Since the proposed method works directly on unstructured surface point clouds, it provides a promising approach for simulations on image-derived geometries, such as in biological morphogenesis from microscopy videos.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-02 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn).
Pagina del lavoro: https://arxiv.org/abs/2609.00216 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T06:52:44.043Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).