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Preprints, Working Papers, ... Year : 2024

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

Abstract

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.
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Dates and versions

hal-04523572 , version 1 (27-03-2024)
hal-04523572 , version 2 (02-08-2024)

Identifiers

  • HAL Id : hal-04523572 , version 2

Cite

Bruce M Boghosian, François Dubois, Pierre Lallemand. Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations. 2024. ⟨hal-04523572v2⟩
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