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Pré-Publication, Document De Travail Année : 2024

Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations

Résumé

Is it possible to consider a lattice Boltzmann scheme as an approximation of a partial differential equation? For a nonhomogeneous advection problem in one spatial dimension, we propose equivalent partial differential equations at various orders. We compare the lattice Boltzmann results and a spectral approximation of the differential equations. No simple correlation is obtained for a stationary problem. For an unsteady situation, we show that the initialization scheme of the microscopic moments plays a crucial role.
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hal-04523572 , version 1 (27-03-2024)

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  • HAL Id : hal-04523572 , version 1

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Bruce M Boghosian, François Dubois, Pierre Lallemand. Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations. 2024. ⟨hal-04523572⟩
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