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PreprintCC BY-NC-ND 4.0HAL

A flux form semi lagrangian scheme for the transport equation on reduced 2D grids

  • Clément Lasuen
  • Fabrice Voitus
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Abstract

This works presents a new Flux Form Semi Lagrangian scheme for the transport equations. It is an extension of the one dimensionnal FFSL scheme presented in [LR96, LLM96]. The scheme they proposed is conservative and positive under a Lipschitz condition. Here we extend it to the two dimensional case on reduced grids. The scheme we obtain is conservative and its positivity condition is the minimum of the Lipschitz condition in each direction. Besides, we propose another computation of the tracer concentration that uses the same trajectories as the density computation.

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Cite

BibTeXRIS
BibTeX
@misc{lasuen2026flux,
  title = {{A flux form semi lagrangian scheme for the transport equation on reduced 2D grids}},
  author = {Clément Lasuen and Fabrice Voitus},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05843273v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A flux form semi lagrangian scheme for the transport equation on reduced 2D grids
AU  - Clément Lasuen
AU  - Fabrice Voitus
PY  - 2026
DA  - 2026/10/23
PB  - HAL
UR  - https://hal.science/hal-05843273v1
AB  - This works presents a new Flux Form Semi Lagrangian scheme for the transport equations. It is an extension of the one dimensionnal FFSL scheme presented in [LR96, LLM96]. The scheme they proposed is conservative and positive under a Lipschitz condition. Here we extend it to the two dimensional case on reduced grids. The scheme we obtain is conservative and its positivity condition is the minimum of the Lipschitz condition in each direction. Besides, we propose another computation of the tracer concentration that uses the same trajectories as the density computation.
ER  -