Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics
Abstract
One-Fluid Two-Temperature Euler (OFTT-Euler) equations are used for modeling non-equilibrium hydrodynamics and form a system of nonlinear hyperbolic partial differential equations with non-conservative products. The model decomposed the total pressure into two scalar components: one for electrons and one for ions. In this work, we design entropy-stable finite difference numerical schemes for the model. This is achieved by introducing a novel reformulation of the equations, ensuring that the new non-conservative terms do not contribute to the entropy evolution. For this novel reformulation of the equations, we design higher-order entropy-conservative numerical schemes by using Tadmor's relation for the conservative part and higher-order central differences for the non-conservative parts. Finally, we design the entropy-dissipation terms using the entropy-scaled right eigenvectors of the conservative part, thereby ensuring entropy stability for the entire system at the semi-discrete level. We present several test cases in one and two dimensions to demonstrate the accuracy and entropy stability of the proposed schemes.
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BibTeX
@misc{singh2026entropy,
title = {{Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics}},
author = {Chetan Singh and Harish Kumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.15616},
eprint = {2605.15616},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15616},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics
AU - Chetan Singh
AU - Harish Kumar
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2605.15616
UR - https://arxiv.org/abs/2605.15616
AB - One-Fluid Two-Temperature Euler (OFTT-Euler) equations are used for modeling non-equilibrium hydrodynamics and form a system of nonlinear hyperbolic partial differential equations with non-conservative products. The model decomposed the total pressure into two scalar components: one for electrons and one for ions. In this work, we design entropy-stable finite difference numerical schemes for the model. This is achieved by introducing a novel reformulation of the equations, ensuring that the new non-conservative terms do not contribute to the entropy evolution. For this novel reformulation of the equations, we design higher-order entropy-conservative numerical schemes by using Tadmor's relation for the conservative part and higher-order central differences for the non-conservative parts. Finally, we design the entropy-dissipation terms using the entropy-scaled right eigenvectors of the conservative part, thereby ensuring entropy stability for the entire system at the semi-discrete level. We present several test cases in one and two dimensions to demonstrate the accuracy and entropy stability of the proposed schemes.
ER -