Comptes Rendus
Discrete simulation of fluid dynamics
Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion
Comptes Rendus. Mécanique, Volume 343 (2015) no. 10-11, pp. 518-532.

This work demonstrates that in advection–diffusion Lattice Boltzmann schemes, the local mass-conserving boundary rules, such as bounce-back and local specular reflection, may modify the transport coefficients predicted by the Chapman–Enskog expansion when they enforce to zero not only the normal, but also the tangential boundary flux. In order to accommodate it to the bulk solution, the system develops a Knudsen-layer correction to the non-equilibrium part of the population solution. Two principal secondary effects—(i) decrease in the diffusion coefficient, and (ii) retardation of the average advection velocity, obtained in a closed analytical form, are proportional, respectively, to freely assigned diagonal weights for equilibrium mass and velocity terms. In addition, due to their transverse velocity gradients, the boundary layers affect the longitudinal diffusion coefficient similarly to Taylor dispersion, as they grow as the square of the Péclet number. These numerical artifacts can be eliminated or reduced by a proper space distribution of the free-tunable collision eigenvalue in two-relaxation-time schemes.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2015.03.004
Keywords: Normal flux boundary condition, Advection–diffusion lattice Boltzmann schemes, Boundary layer, Tangential flux, Pure diffusion, Taylor dispersion, Boundary-layer dispersion, Equilibrium weights, Two-relaxation-time LBM scheme, Recurrence equations, Exact solutions of numerical scheme

Irina Ginzburg 1; Laetitia Roux 1; Goncalo Silva 1

1 IRSTEA, Antony Regional Centre, HBAN, 1, rue Pierre-Gilles-de-Gennes, CS 10030, 92761 Antony cedex, France
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Irina Ginzburg; Laetitia Roux; Goncalo Silva. Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion. Comptes Rendus. Mécanique, Volume 343 (2015) no. 10-11, pp. 518-532. doi : 10.1016/j.crme.2015.03.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.03.004/

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