Review of thermodynamic structures and structure-preserving discretisations of Cahn--Hilliard-type models
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911434793811968 |
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| author | Brunk, Aaron Eikelder, Marco F. P. ten Fritz, Marvin Höhn, Dennis Trautwein, Dennis |
| author_facet | Brunk, Aaron Eikelder, Marco F. P. ten Fritz, Marvin Höhn, Dennis Trautwein, Dennis |
| contents | The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic structures underlying these models, focusing on the formulation of free energy functionals, dissipation mechanisms, and variational principles. We compare structural properties, emphasizing how these models encode conservation laws and energy dissipation. A central theme is the translation of these thermodynamic structures into numerical practice by providing representative discretisation strategies that aim to preserve mass conservation, stability, and energy decay. Particular attention is paid to the trade-offs between accuracy, efficiency, and structure preservation in large-scale simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08791 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Review of thermodynamic structures and structure-preserving discretisations of Cahn--Hilliard-type models Brunk, Aaron Eikelder, Marco F. P. ten Fritz, Marvin Höhn, Dennis Trautwein, Dennis Numerical Analysis The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic structures underlying these models, focusing on the formulation of free energy functionals, dissipation mechanisms, and variational principles. We compare structural properties, emphasizing how these models encode conservation laws and energy dissipation. A central theme is the translation of these thermodynamic structures into numerical practice by providing representative discretisation strategies that aim to preserve mass conservation, stability, and energy decay. Particular attention is paid to the trade-offs between accuracy, efficiency, and structure preservation in large-scale simulations. |
| title | Review of thermodynamic structures and structure-preserving discretisations of Cahn--Hilliard-type models |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.08791 |