Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929610614112256 |
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| author | Kummer, Eliane Simonis, Stephan |
| author_facet | Kummer, Eliane Simonis, Stephan |
| contents | Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1-40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work, we provide counterexamples for the conjecture that any multi-step finite difference scheme has a unique lattice Boltzmann formulation. Based on that, we indicate the existence of equivalence classes for discretized relaxation systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_01494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods Kummer, Eliane Simonis, Stephan Numerical Analysis Mathematical Physics 65M06, 76M28 Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1-40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work, we provide counterexamples for the conjecture that any multi-step finite difference scheme has a unique lattice Boltzmann formulation. Based on that, we indicate the existence of equivalence classes for discretized relaxation systems. |
| title | Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods |
| topic | Numerical Analysis Mathematical Physics 65M06, 76M28 |
| url | https://arxiv.org/abs/2412.01494 |