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PreprintarXiv licencearXiv

Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state

  • Nicolas Favrie
  • Matthias Maier
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Abstract

We derive computable upper bounds on the maximum wave speed in the Riemann problem for the compressible Euler equations with a composite equation of state, in which the pressure is the sum of a convex hydrodynamical part and a barotropic correction. The correction may destroy the convexity of the equation of state, so that the Riemann solution can contain composite shock-rarefaction waves. The bounds are obtained by comparison with the auxiliary Riemann problem for the hydrodynamical equation of state alone. The bounds hold irrespective of whether the outer waves are elementary or composite and require no case distinction on the wave type.

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Cite

BibTeXRIS
BibTeX
@misc{favrie2026guaranteed,
  title = {{Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state}},
  author = {Nicolas Favrie and Matthias Maier},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14287},
  eprint = {2609.14287},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14287},
}
RIS
TY  - UNPB
TI  - Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state
AU  - Nicolas Favrie
AU  - Matthias Maier
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.14287
UR  - https://arxiv.org/abs/2609.14287
AB  - We derive computable upper bounds on the maximum wave speed in the Riemann problem for the compressible Euler equations with a composite equation of state, in which the pressure is the sum of a convex hydrodynamical part and a barotropic correction. The correction may destroy the convexity of the equation of state, so that the Riemann solution can contain composite shock-rarefaction waves. The bounds are obtained by comparison with the auxiliary Riemann problem for the hydrodynamical equation of state alone. The bounds hold irrespective of whether the outer waves are elementary or composite and require no case distinction on the wave type.
ER  -