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PreprintCC BY-NC-SA 4.0arXiv

On Enhancing the Dissipative Behavior of Active Flux Advection Schemes

  • Christian Klingenberg
  • Simon Krotsch
  • Philip Roe
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Abstract

In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing four additional parameters R, S, T, and U that allow the numerical dissipation and dispersion of the scheme to be adjusted. The influence of these parameters is studied using Fourier analysis and parameter choices that lead to schemes with improved dissipative properties are identified. These improvements are validated by numerical experiments.

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Cite

BibTeXRIS
BibTeX
@misc{klingenberg2026enhancing,
  title = {{On Enhancing the Dissipative Behavior of Active Flux Advection Schemes}},
  author = {Christian Klingenberg and Simon Krotsch and Philip Roe},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.09669},
  eprint = {2605.09669},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.09669},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - On Enhancing the Dissipative Behavior of Active Flux Advection Schemes
AU  - Christian Klingenberg
AU  - Simon Krotsch
AU  - Philip Roe
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2605.09669
UR  - https://arxiv.org/abs/2605.09669
AB  - In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing four additional parameters R, S, T, and U that allow the numerical dissipation and dispersion of the scheme to be adjusted. The influence of these parameters is studied using Fourier analysis and parameter choices that lead to schemes with improved dissipative properties are identified. These improvements are validated by numerical experiments.
ER  -