Exact moment models for conservation laws in phase space
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917274089160704 |
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| author | Mukhamet, Tileuzhan Kormann, Katharina |
| author_facet | Mukhamet, Tileuzhan Kormann, Katharina |
| contents | Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain extent. To derive moment equations, we use a parameterization of the distribution function using centered moments, as proposed by Burby. This yields moment equations for which the parameterized distribution function exactly solves the hyperbolic conservation law. Similarly, a particle model is derived based on a parametrization of the distribution function using phase space moments. Finally, we present the application of the method to the non-relativistic and relativistic Vlasov--Maxwell equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact moment models for conservation laws in phase space Mukhamet, Tileuzhan Kormann, Katharina Plasma Physics 35L65, 35Q49, 35Q83 Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain extent. To derive moment equations, we use a parameterization of the distribution function using centered moments, as proposed by Burby. This yields moment equations for which the parameterized distribution function exactly solves the hyperbolic conservation law. Similarly, a particle model is derived based on a parametrization of the distribution function using phase space moments. Finally, we present the application of the method to the non-relativistic and relativistic Vlasov--Maxwell equations. |
| title | Exact moment models for conservation laws in phase space |
| topic | Plasma Physics 35L65, 35Q49, 35Q83 |
| url | https://arxiv.org/abs/2602.13180 |