Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods
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 schem...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
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| Series: | Examples and Counterexamples |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000375 |
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| Summary: | 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. |
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| ISSN: | 2666-657X |