A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection
Abstract
This paper proposes a novel discretely entropy conserving/stable flux reconstruction (FR) scheme for nonlinear conservation laws. The scheme combines a hybridized split-form differential operator with a generalized entropy projection, enabling discrete entropy conservation for arbitrary nodal distributions and arbitrary correction functions without modifying the original quadrature weights. The formulation is built directly upon the classical FR framework and is shown to preserve conservation properties while achieving entropy conservation in the semi-discrete sense. Numerical experiments using the isentropic vortex problem confirm the theoretically predicted accuracy and demonstrate robust entropy behavior with entropy-dissipative interface fluxes.
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BibTeX
@misc{liang2026discretely,
title = {{A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection}},
author = {Geng Liang and Junjie Wang and Hui Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24257},
eprint = {2609.24257},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24257},
}
RIS
TY - UNPB
TI - A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection
AU - Geng Liang
AU - Junjie Wang
AU - Hui Xu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24257
UR - https://arxiv.org/abs/2609.24257
AB - This paper proposes a novel discretely entropy conserving/stable flux reconstruction (FR) scheme for nonlinear conservation laws. The scheme combines a hybridized split-form differential operator with a generalized entropy projection, enabling discrete entropy conservation for arbitrary nodal distributions and arbitrary correction functions without modifying the original quadrature weights. The formulation is built directly upon the classical FR framework and is shown to preserve conservation properties while achieving entropy conservation in the semi-discrete sense. Numerical experiments using the isentropic vortex problem confirm the theoretically predicted accuracy and demonstrate robust entropy behavior with entropy-dissipative interface fluxes.
ER -