Structure-preserving approximation for non-isothermal phase-field models in melt flow
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917431241342976 |
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| author | Brunk, Aaron Höhn, Dennis |
| author_facet | Brunk, Aaron Höhn, Dennis |
| contents | This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The system comprises the incompressible Navier-Stokes equations coupled with the non-isothermal Allen-Cahn equation, which includes a non-conserved phase-field equation and a temperature equation. The proposed numerical scheme preserves entropy production exactly and maintains total energy conservation up to a negative numerical dissipation. Convergence tests in both space and time are conducted, and representative examples are provided to demonstrate the scheme's effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21697 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure-preserving approximation for non-isothermal phase-field models in melt flow Brunk, Aaron Höhn, Dennis Numerical Analysis This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The system comprises the incompressible Navier-Stokes equations coupled with the non-isothermal Allen-Cahn equation, which includes a non-conserved phase-field equation and a temperature equation. The proposed numerical scheme preserves entropy production exactly and maintains total energy conservation up to a negative numerical dissipation. Convergence tests in both space and time are conducted, and representative examples are provided to demonstrate the scheme's effectiveness. |
| title | Structure-preserving approximation for non-isothermal phase-field models in melt flow |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.21697 |