Solving the Porous Medium Equation with the eXtreme Mesh deformation approach (X-Mesh)
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910773781987328 |
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| author | Chemin, Alexandre Lambrechts, Jonathan Moës, Nicolas Remacle, Jean-François |
| author_facet | Chemin, Alexandre Lambrechts, Jonathan Moës, Nicolas Remacle, Jean-François |
| contents | We introduce a new scheme for solving the non-regularized Porous Medium Equation. It is mass conserving and uses only positive unknown values. To address these typically conflicting features, we employ the eXtreme Mesh deformation approach (X-Mesh), specifically designed for problems involving sharp interfaces. The method ensures that the interface is always meshed, even in the face of complex topological changes, without the need for remeshing or altering the mesh topology. We illustrate the effectiveness of the approach through various numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Porous Medium Equation with the eXtreme Mesh deformation approach (X-Mesh) Chemin, Alexandre Lambrechts, Jonathan Moës, Nicolas Remacle, Jean-François Numerical Analysis We introduce a new scheme for solving the non-regularized Porous Medium Equation. It is mass conserving and uses only positive unknown values. To address these typically conflicting features, we employ the eXtreme Mesh deformation approach (X-Mesh), specifically designed for problems involving sharp interfaces. The method ensures that the interface is always meshed, even in the face of complex topological changes, without the need for remeshing or altering the mesh topology. We illustrate the effectiveness of the approach through various numerical experiments. |
| title | Solving the Porous Medium Equation with the eXtreme Mesh deformation approach (X-Mesh) |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.03083 |