An asymptotic preserving kinetic scheme for the M1 model of linear transport
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929280188940288 |
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| author | Jean-Luc, Feugeas Julien, Mathiaud Luc, Mieussens Thomas, Vigier |
| author_facet | Jean-Luc, Feugeas Julien, Mathiaud Luc, Mieussens Thomas, Vigier |
| contents | Moment models with suitable closure can lead to accurate and computationally efficient solvers for particle transport. Hence, we propose a new asymptotic preserving scheme for the M1 model of linear transport that works uniformly for any Knudsen number. Our idea is to apply the M1 closure at the numerical level to an existing asymptotic preserving scheme for the corresponding kinetic equation, namely the Unified Gas Kinetic scheme (UGKS) originally proposed in [27] and extended to linear transport in [24]. In order to ensure the moments realizability in this new scheme, the UGKS positivity needs to be maintained. We propose a new density reconstruction in time to obtain this property. A second order extension is also suggested and validated. Several test cases show the performances of this new scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An asymptotic preserving kinetic scheme for the M1 model of linear transport Jean-Luc, Feugeas Julien, Mathiaud Luc, Mieussens Thomas, Vigier Numerical Analysis Mathematical Physics Moment models with suitable closure can lead to accurate and computationally efficient solvers for particle transport. Hence, we propose a new asymptotic preserving scheme for the M1 model of linear transport that works uniformly for any Knudsen number. Our idea is to apply the M1 closure at the numerical level to an existing asymptotic preserving scheme for the corresponding kinetic equation, namely the Unified Gas Kinetic scheme (UGKS) originally proposed in [27] and extended to linear transport in [24]. In order to ensure the moments realizability in this new scheme, the UGKS positivity needs to be maintained. We propose a new density reconstruction in time to obtain this property. A second order extension is also suggested and validated. Several test cases show the performances of this new scheme. |
| title | An asymptotic preserving kinetic scheme for the M1 model of linear transport |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2305.02804 |