Entropy dissipative high order schemes for a hyperbolic model of two-layer thin film flow
Abstract
In this article, we develop high-order, entropy-dissipative schemes for a hyperbolic system of conservation laws describing the first-order dynamics of two-layer thin-film flows of immiscible fluids with perfectly soluble solute particles. The key aspect is to construct entropy-conservative fluxes in the sense of Tadmor. Here, we consider and compare two different construction processes: an exact formulation and a commonly used simplified approximation in the flux evaluation. While the approximate approach is simpler at the level of construction and is frequently employed in practice (also in other contexts), it is less structured, leading to increased computational cost in the implementation compared to the exact formulation, which has been much more complicated to derive. We employ these fluxes within both an entropy-dissipative finite-difference framework and an entropy-dissipative discontinuous Galerkin spectral element method. Through numerical experiments using two distinct spatial discretizations, we investigate the performance and robustness of the proposed methods and demonstrate that the choice of numerical flux has a noticeable impact on the efficiency of the resulting solvers.
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BibTeX
@misc{barthwal2026entropy,
title = {{Entropy dissipative high order schemes for a hyperbolic model of two-layer thin film flow}},
author = {Rahul Barthwal and Philipp Öffner and Chetan Singh and Jan Zawallich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02059},
eprint = {2610.02059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02059},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entropy dissipative high order schemes for a hyperbolic model of two-layer thin film flow
AU - Rahul Barthwal
AU - Philipp Öffner
AU - Chetan Singh
AU - Jan Zawallich
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02059
UR - https://arxiv.org/abs/2610.02059
AB - In this article, we develop high-order, entropy-dissipative schemes for a hyperbolic system of conservation laws describing the first-order dynamics of two-layer thin-film flows of immiscible fluids with perfectly soluble solute particles. The key aspect is to construct entropy-conservative fluxes in the sense of Tadmor. Here, we consider and compare two different construction processes: an exact formulation and a commonly used simplified approximation in the flux evaluation. While the approximate approach is simpler at the level of construction and is frequently employed in practice (also in other contexts), it is less structured, leading to increased computational cost in the implementation compared to the exact formulation, which has been much more complicated to derive. We employ these fluxes within both an entropy-dissipative finite-difference framework and an entropy-dissipative discontinuous Galerkin spectral element method. Through numerical experiments using two distinct spatial discretizations, we investigate the performance and robustness of the proposed methods and demonstrate that the choice of numerical flux has a noticeable impact on the efficiency of the resulting solvers.
ER -