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

Imad Kissami, Moussa Ziggaf, Wassim Aboussi, Mohamed Boubekeur and Fahd Kalloubi

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 475-496

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.

Keywords: Hyperbolic conservation laws; Finite volume methods; Machine learning; Numerical flux selection; Data-driven approach (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426001564
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:475-496

DOI: 10.1016/j.matcom.2026.04.014

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().