Letter to the Editor: Truncation errors of the D3Q19 lattice model for the lattice Boltzmann method. Bauer, M., Silva, G., & Rüde, U. Journal of Computational Physics, November, 2019. MMC. "Jupyter notebook with steady state Chapman Enskog Analysis of D3Q19 equilibria using computer algebra system sympy": https://ars.els-cdn.com/content/image/1-s2.0-S0021999119308162-mmc1.zip
We comment on the truncation error analysis and numerical artifacts of the D3Q19 lattice Boltzmann model reported in Silva et al.[3]. We present corrections for specific spatial truncation error terms in the momentum conservation equations. By introducing an improved discrete equilibrium for the D3Q19 stencil, we show that the reported spurious currents in a square channel duct flow are caused by the form of the discrete equilibrium and are not due to the structure and isotropy properties of the D3Q19 velocity set itself. Numerical experiments on a square channel and a more complex nozzle geometry confirm these results.
@article{bauer_letter_2019,
title = {Letter to the {Editor}: {Truncation} errors of the {D3Q19} lattice model for the lattice {Boltzmann} method},
issn = {00219991},
shorttitle = {Letter to the {Editor}},
doi = {10.1016/j.jcp.2019.109111},
abstract = {We comment on the truncation error analysis and numerical artifacts of the D3Q19 lattice Boltzmann model reported in Silva et al.[3]. We present corrections for specific spatial truncation error terms in the momentum conservation equations. By introducing an improved discrete equilibrium for the D3Q19 stencil, we show that the reported spurious currents in a square channel duct flow are caused by the form of the discrete equilibrium and are not due to the structure and isotropy properties of the D3Q19 velocity set itself. Numerical experiments on a square channel and a more complex nozzle geometry confirm these results.},
language = {en},
urldate = {2019-11-23},
journal = {Journal of Computational Physics},
author = {Bauer, Martin and Silva, Goncalo and Rüde, Ulrich},
month = nov,
year = {2019},
note = {MMC. "Jupyter notebook with steady state Chapman Enskog Analysis of D3Q19 equilibria using computer algebra system sympy":
https://ars.els-cdn.com/content/image/1-s2.0-S0021999119308162-mmc1.zip},
keywords = {Lattice Boltzmann, uses sympy},
pages = {109111},
}