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A data-driven approach for flux selection in finite volume methods for hyperbolic conservation laws

Author

Listed:
  • Kissami, Imad
  • Ziggaf, Moussa
  • Aboussi, Wassim
  • Boubekeur, Mohamed
  • Kalloubi, Fahd

Abstract

Selecting the most suitable scheme in a numerical simulation has been a long standing problem, as most schemes are not designed to handle all types of simulation scenarios. Traditional methods are typically designed for a specific physical features and are not generally applicable to all simulation problems. To address this generalization gap, we propose a data-driven approach that selects, at each spatial point and time step, the most appropriate numerical flux from a predefined set of classical finite-volume schemes. We then evaluate the proposed method on a broad set of classical test cases for Euler equations of an ideal gas, demonstrating strong generalization across diverse flow regimes while maintaining stability and accuracy, particularly in capturing discontinuities.

Suggested Citation

  • Kissami, Imad & Ziggaf, Moussa & Aboussi, Wassim & Boubekeur, Mohamed & Kalloubi, Fahd, 2026. "A data-driven approach for flux selection in finite volume methods for hyperbolic conservation laws," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 475-496.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:475-496
    DOI: 10.1016/j.matcom.2026.04.014
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    References listed on IDEAS

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    1. Aboussi, Wassim & Ziggaf, Moussa & Kissami, Imad & Boubekeur, Mohamed, 2023. "A highly efficient finite volume method with a diffusion control parameter for hyperbolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 177-193.
    2. Yubiao Sun & Qiankun Sun & Kan Qin, 2021. "Physics-Based Deep Learning for Flow Problems," Energies, MDPI, vol. 14(22), pages 1-24, November.
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