Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917864447934464 |
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| author | Boghosian, Bruce M Dubois, François Lallemand, Pierre |
| author_facet | Boghosian, Bruce M Dubois, François Lallemand, Pierre |
| contents | In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We first derive a family of equivalent partial differential equations at various orders, and we compare the lattice Boltzmann experimental results with a spectral approximation of the differential equations. For an unsteady situation, we show that the initialization scheme at a sufficiently high order of the microscopic moments plays a crucial role to observe an asymptotic error consistent with the order of approximation. For a stationary long-time limit, we observe that the measured asymptotic error converges with a reduced order of precision compared to the one suggested by asymptotic analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations Boghosian, Bruce M Dubois, François Lallemand, Pierre Numerical Analysis In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We first derive a family of equivalent partial differential equations at various orders, and we compare the lattice Boltzmann experimental results with a spectral approximation of the differential equations. For an unsteady situation, we show that the initialization scheme at a sufficiently high order of the microscopic moments plays a crucial role to observe an asymptotic error consistent with the order of approximation. For a stationary long-time limit, we observe that the measured asymptotic error converges with a reduced order of precision compared to the one suggested by asymptotic analysis. |
| title | Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.19231 |