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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.13097 |
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| _version_ | 1866908370490884096 |
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| author | Luddens, Francky Lothodé, Corentin Danaila, Ionut |
| author_facet | Luddens, Francky Lothodé, Corentin Danaila, Ionut |
| contents | Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM) to solve the Stefan problem using a regularized total enthalpy model. The liquid fraction is treated as a nonlinear source/sink term, that involves the time derivative of the solution. The resulting non-linear system is solved using a Newton algorithm. By conserving the locality of the problem, this method is highly scalable, while keeping a high accuracy. The newly developed scheme is analyzed theoretically through a Chapman-Enskog expansion and illustrated numerically with 1D and 2D benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An implicit regularized enthalpy Lattice Boltzmann Method for the Stefan problem Luddens, Francky Lothodé, Corentin Danaila, Ionut Numerical Analysis Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM) to solve the Stefan problem using a regularized total enthalpy model. The liquid fraction is treated as a nonlinear source/sink term, that involves the time derivative of the solution. The resulting non-linear system is solved using a Newton algorithm. By conserving the locality of the problem, this method is highly scalable, while keeping a high accuracy. The newly developed scheme is analyzed theoretically through a Chapman-Enskog expansion and illustrated numerically with 1D and 2D benchmarks. |
| title | An implicit regularized enthalpy Lattice Boltzmann Method for the Stefan problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.13097 |