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Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators

  • Christiane Helzel
  • Mária Lukáčová-Medvid'ová
  • Amelie Porfetye
  • Zhuyan Tang
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Abstract

We present new fully discrete Cartesian grid Active Flux methods for the two-dimensional Euler equations of gas dynamics. A key component of these methods is the evolution operator used to evolve point-value degrees of freedom. Therefore, we derive several new, third-order accurate, multidimensional evolution operators for point-value updates of the linearized Euler equations using the method of bicharacteristics. We also investigate how the reconstruction and choice of approximate evolution operator affect the accuracy and stability of the resulting methods.

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Cite

BibTeXRIS
BibTeX
@misc{helzel2026fully,
  title = {{Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators}},
  author = {Christiane Helzel and Mária Lukáčová-Medvid'ová and Amelie Porfetye and Zhuyan Tang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34669},
  eprint = {2609.34669},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34669},
}
RIS
TY  - UNPB
TI  - Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators
AU  - Christiane Helzel
AU  - Mária Lukáčová-Medvid'ová
AU  - Amelie Porfetye
AU  - Zhuyan Tang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34669
UR  - https://arxiv.org/abs/2609.34669
AB  - We present new fully discrete Cartesian grid Active Flux methods for the two-dimensional Euler equations of gas dynamics. A key component of these methods is the evolution operator used to evolve point-value degrees of freedom. Therefore, we derive several new, third-order accurate, multidimensional evolution operators for point-value updates of the linearized Euler equations using the method of bicharacteristics. We also investigate how the reconstruction and choice of approximate evolution operator affect the accuracy and stability of the resulting methods.
ER  -