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A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity — arXiv:2608.03115

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.03115
License (as archived): CC0-1.0
Archived: 2026-10-31T12:54:24.072Z
SHA-256 of the archived text: 90728be5c79159ae5f6030c75ec5ac0d1eef65e94f076f404ebed78dabf6f666
Stable URL of this page: https://metraipolis.com/documento/dc_33db33713e1a

How to cite

A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity — arXiv:2608.03115 — arXiv (en), https://arxiv.org/abs/2608.03115 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_33db33713e1a (Metraipolis archive dc_33db33713e1a, sha256 90728be5c79159ae5f6030c75ec5ac0d1eef65e94f076f404ebed78dabf6f666)

BibTeX

@misc{dc33db33713e1a,
  title = {A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity — arXiv:2608.03115},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.03115},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_33db33713e1a; sha256 90728be5c79159ae5f6030c75ec5ac0d1eef65e94f076f404ebed78dabf6f666},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.03115. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a gravity-consistent arbitrary Lagrangian--Eulerian finite element method for incompressible Navier--Stokes free-boundary problems with moving contact lines. A direct body-force discretization of gravity may fail to ensure consistency between the discrete gravitational work and the variation of the gravitational potential energy on the evolving domain, resulting in an artificial consistency error and persistent spurious velocities near equilibrium. To remove this inconsistency, we reformulate the gravitational potential energy variation as a moving-boundary integral over intermediate ALE configurations and evaluate it exactly using Simpson's quadrature rule. This leads to a mildly nonlinear fully discrete scheme in which the gravitational contribution is exactly consistent with the discrete potential-energy variation. The proposed method preserves volume exactly, satisfies a discrete energy-dissipation law including gravitational potential energy, and under suitable assumptions, drives the discrete velocity to zero in the long-time regime, thereby excluding persistent gravity-induced spurious velocities. Together with the BGN treatment of the free surface and the MDR bulk mesh extension, the scheme maintains accurate interface tracking and good mesh quality near the moving contact line. Numerical experiments in two and three spatial dimensions confirm the theoretical properties.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-05 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.03115 — 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 2026-10-31T12:42:33.376Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-05?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).