Extended-regularized lattice Boltzmann method
Abstract
Regularized lattice Boltzmann methods improve numerical stability by projecting the nonequilibrium distribution onto its hydrodynamic second-order Hermite sector and filtering the remaining kinetic modes. We introduce a separate relaxation time for the complete complementary kinetic subspace. The resulting extended-regularized lattice Boltzmann method (E-RLBM) interpolates continuously between the Bhatnagar-Gross-Krook and regularized collision operators while retaining a two-rate implementation. A Chapman-Enskog expansion shows that the isothermal Navier-Stokes equations are recovered with kinematic viscosity ν=cs2(τ−Δt/2), independently of the kinetic relaxation time τnh, whereas τnh changes higher-order truncation errors. For linear transverse shear, its first effect is a fourth-derivative term whose coefficient depends on the direction of propagation relative to the lattice. This fourth-order coefficient is affine in τnh. For linear shear on D2Q9 and τnh between τ and Δt, it lies between the corresponding BGK and RLBM values in every propagation direction. Stability maps for the decaying Taylor-Green vortex and flow past a rectangular obstacle show that an appropriate kinetic relaxation substantially enlarges the stable parameter domain. In a Taylor-Green convergence test with consistent initialization, all three operators converge at second order, and their error differences follow the hyperviscous coefficient for diagonal shear waves: the E-RLBM error is about 6% above the BGK error and about 40% below the RLBM error; in a double shear layer at Re = 80000, the E-RLBM follows the RLBM convergence curve. The proposed collision operator therefore provides a low-cost means of controlling nonhydrodynamic modes without introducing a full multiple-relaxation-time basis.
Related
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BibTeX
@misc{santos2026extendedregularized,
title = {{Extended-regularized lattice Boltzmann method}},
author = {Luís Orlando Emerich dos Santos and Diogo Nardelli Siebert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31072},
eprint = {2610.31072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31072},
}
RIS
TY - UNPB
TI - Extended-regularized lattice Boltzmann method
AU - Luís Orlando Emerich dos Santos
AU - Diogo Nardelli Siebert
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31072
UR - https://arxiv.org/abs/2610.31072
AB - Regularized lattice Boltzmann methods improve numerical stability by projecting the nonequilibrium distribution onto its hydrodynamic second-order Hermite sector and filtering the remaining kinetic modes. We introduce a separate relaxation time for the complete complementary kinetic subspace. The resulting extended-regularized lattice Boltzmann method (E-RLBM) interpolates continuously between the Bhatnagar-Gross-Krook and regularized collision operators while retaining a two-rate implementation. A Chapman-Enskog expansion shows that the isothermal Navier-Stokes equations are recovered with kinematic viscosity ν=c_s^2(τ−Δt/2), independently of the kinetic relaxation time τ_nh, whereas τ_nh changes higher-order truncation errors. For linear transverse shear, its first effect is a fourth-derivative term whose coefficient depends on the direction of propagation relative to the lattice. This fourth-order coefficient is affine in τ_nh. For linear shear on D2Q9 and τ_nh between τ and Δt, it lies between the corresponding BGK and RLBM values in every propagation direction. Stability maps for the decaying Taylor-Green vortex and flow past a rectangular obstacle show that an appropriate kinetic relaxation substantially enlarges the stable parameter domain. In a Taylor-Green convergence test with consistent initialization, all three operators converge at second order, and their error differences follow the hyperviscous coefficient for diagonal shear waves: the E-RLBM error is about 6% above the BGK error and about 40% below the RLBM error; in a double shear layer at Re = 80000, the E-RLBM follows the RLBM convergence curve. The proposed collision operator therefore provides a low-cost means of controlling nonhydrodynamic modes without introducing a full multiple-relaxation-time basis.
ER -