A new formulation of Discontinuous Galerkin method for interface capturing approaches

Abstract

In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint--Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier--Stokes equations with surface tension, discretized using the standard P2−P1 Taylor--Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh--Taylor instability.

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BibTeX RIS

BibTeX

@misc{herri2026formulation,
  title = {{A new formulation of Discontinuous Galerkin method for interface capturing approaches}},
  author = {W. Herri and K. Benmoussa and R. Bouydou and D. Yakoubi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07327},
  eprint = {2609.07327},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07327},
  note = {CC0},
}

RIS

TY  - UNPB
TI  - A new formulation of Discontinuous Galerkin method for interface capturing approaches
AU  - W. Herri
AU  - K. Benmoussa
AU  - R. Bouydou
AU  - D. Yakoubi
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07327
UR  - https://arxiv.org/abs/2609.07327
AB  - In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint--Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier--Stokes equations with surface tension, discretized using the standard P2−P1 Taylor--Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh--Taylor instability.
ER  -

Abstract

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