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PreprintCC BY 4.0arXiv

Entropy-Based Local Characteristic Decomposition

  • Shaoshuai Chu
  • Michael Herty
  • Alexander Kurganov
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Abstract

Local characteristic decomposition (LCD) is widely used in high-order numerical methods for hyperbolic systems of conservation laws to reduce spurious oscillations appearing in the computed solutions. The LCD implementation requires a representative average interface state, typically obtained using arithmetic or Roe-type averages of the nearly grid values. We propose an entropy-based LCD (ELCD), in which the states in the two cells adjacent to an interface are considered together with several nearby states in phase space. Among these candidates, we select the state that locally minimizes the entropy and use it as an average interface state for linearizing the flux Jacobian. We incorporate the ELCD into several second-order finite-volume and fifth-order finite-difference schemes. Numerical experiments for the two-dimensional Euler equations of gas dynamics show that the schemes, which utilize the ELCD procedure generally resolve complex wave structures more sharply than their counterparts, which use the arithmetic averages.

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Cite

BibTeXRIS
BibTeX
@misc{chu2026entropybased,
  title = {{Entropy-Based Local Characteristic Decomposition}},
  author = {Shaoshuai Chu and Michael Herty and Alexander Kurganov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19838},
  eprint = {2609.19838},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19838},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entropy-Based Local Characteristic Decomposition
AU  - Shaoshuai Chu
AU  - Michael Herty
AU  - Alexander Kurganov
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19838
UR  - https://arxiv.org/abs/2609.19838
AB  - Local characteristic decomposition (LCD) is widely used in high-order numerical methods for hyperbolic systems of conservation laws to reduce spurious oscillations appearing in the computed solutions. The LCD implementation requires a representative average interface state, typically obtained using arithmetic or Roe-type averages of the nearly grid values. We propose an entropy-based LCD (ELCD), in which the states in the two cells adjacent to an interface are considered together with several nearby states in phase space. Among these candidates, we select the state that locally minimizes the entropy and use it as an average interface state for linearizing the flux Jacobian. We incorporate the ELCD into several second-order finite-volume and fifth-order finite-difference schemes. Numerical experiments for the two-dimensional Euler equations of gas dynamics show that the schemes, which utilize the ELCD procedure generally resolve complex wave structures more sharply than their counterparts, which use the arithmetic averages.
ER  -