Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929546285023232 |
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| author | Suciu, Nicolae Nepal, Surendra Wondmagegne, Yosief Ögren, Magnus Muntean, Adrian |
| author_facet | Suciu, Nicolae Nepal, Surendra Wondmagegne, Yosief Ögren, Magnus Muntean, Adrian |
| contents | This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its speed. This situation is usually referred to in the literature as moving-boundary problem with kinetic condition. As a direct application, we propose a numerical scheme to forecast the penetration of small diffusants into a rubber-based material. To check the quality of our results, we compare the numerical results obtained by global random walks either using the analytical solution to selected benchmark cases or relying on finite element approximations with a priori known convergence rates. It turns out that the global random walk concept can be used to produce good quality approximations of the weak solutions to the target class of problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results Suciu, Nicolae Nepal, Surendra Wondmagegne, Yosief Ögren, Magnus Muntean, Adrian Numerical Analysis 35R37, 65M75, 65M60 This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its speed. This situation is usually referred to in the literature as moving-boundary problem with kinetic condition. As a direct application, we propose a numerical scheme to forecast the penetration of small diffusants into a rubber-based material. To check the quality of our results, we compare the numerical results obtained by global random walks either using the analytical solution to selected benchmark cases or relying on finite element approximations with a priori known convergence rates. It turns out that the global random walk concept can be used to produce good quality approximations of the weak solutions to the target class of problems. |
| title | Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results |
| topic | Numerical Analysis 35R37, 65M75, 65M60 |
| url | https://arxiv.org/abs/2410.12378 |