A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows
Abstract
Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis Λ=1/4, ω+=ω-=1 makes one collision eliminate all non-hydrodynamic perturbations; η(ν)=|6ν−1|/(6ν+1) vanishes at ν=1/6, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at N=256, Re=1 under matched-accuracy and 1% gates. The matched speedup rises monotonically to 122.02 at N=1024, with gains persisting across Re=10−4--$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at N=128, Re=1. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at Re=10 and 3.84 at Re=100 for N=128. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.
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BibTeX
@misc{ding2026macroscopicshadowcorrected,
title = {{A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows}},
author = {Yanhui Ding and Yaolong Yu and Yuan Yu and Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39474},
eprint = {2609.39474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39474},
}
RIS
TY - UNPB
TI - A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows
AU - Yanhui Ding
AU - Yaolong Yu
AU - Yuan Yu
AU - Hao Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39474
UR - https://arxiv.org/abs/2609.39474
AB - Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis Λ=1/4, ω^+=ω^-=1 makes one collision eliminate all non-hydrodynamic perturbations; η(ν)=|6ν−1|/(6ν+1) vanishes at ν=1/6, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at N=256, Re=1 under matched-accuracy and 1% gates. The matched speedup rises monotonically to 122.02 at N=1024, with gains persisting across Re=10^−4--$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at N=128, Re=1. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at Re=10 and 3.84 at Re=100 for N=128. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.
ER -