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PreprintarXiv licencearXiv

Well-balanced second-order approximation of the compressible atmospheric Euler equations

  • Crystal Farris
  • Matthias Maier
  • Eric J. Tovar
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Abstract

We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to stratified rest states, including isentropic and isothermal equilibria. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density and potential temperature. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and typical benchmark problems for atmospheric flows.

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Cite

BibTeXRIS
BibTeX
@misc{farris2026wellbalanced,
  title = {{Well-balanced second-order approximation of the compressible atmospheric Euler equations}},
  author = {Crystal Farris and Matthias Maier and Eric J. Tovar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.19764},
  eprint = {2606.19764},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19764},
}
RIS
TY  - UNPB
TI  - Well-balanced second-order approximation of the compressible atmospheric Euler equations
AU  - Crystal Farris
AU  - Matthias Maier
AU  - Eric J. Tovar
PY  - 2026
DA  - 2026/10/31
PB  - arXiv
DO  - 10.48550/arxiv.2606.19764
UR  - https://arxiv.org/abs/2606.19764
AB  - We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to stratified rest states, including isentropic and isothermal equilibria. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density and potential temperature. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and typical benchmark problems for atmospheric flows.
ER  -