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This study presents a reformulated simplified lattice Boltzmann method (SLBM) that addresses numerical dissipation, dispersion, and stability issues in computational fluid dynamics simulations. The researchers developed a generalized formulation using a predictor-corrector strategy with tunable parameters, demonstrating that the method maintains second-order accuracy while improving numerical performance and stability, particularly in high-Reynolds-number flows and under-resolved cases. Linear stability analysis and validation tests confirm the method can resolve fine vortex structures on coarser computational grids than traditional approaches.
Why it matters
This advancement enables more efficient and accurate simulations of incompressible flows, which are critical for engineering applications including aerodynamics, turbomachinery design, and environmental fluid mechanics. The improved stability and accuracy on coarser grids could significantly reduce computational costs while maintaining high fidelity in complex flow simulations.
Understand the Science
arXiv:2605.29887v2 Announce Type: replace
Abstract: The simplified lattice Boltzmann method (SLBM) is a recent development in the lattice Boltzmann method (LBM) community, addressing the intrinsic limitations of the traditional LBM by directly evolving macroscopic quantities and maintaining numerical stability in high-Reynolds-number simulations. However, fundamental understanding of the numerical dissipation and dispersion of SLBM is still lacking, and the origin of its good numerical stability is not fully resolved. In this work, a generalized formulation is developed, revealing that the SLBM recovers modified macroscopic equations containing both intrinsic physical deviations and numerical truncation errors. To remove these deviations, the macroscopic equation derived from the standard Bhatnagar–Gross–Krook lattice Boltzmann method (BGK-LBM) is adopted as a reference model and solved by the predictor-corrector strategy, which constitutes the reformulated SLBM. The proposed method uses the generalized SLBM formulation in the predictor step with tunable high-order parameters, while the corrector step is realized by the finite-difference discretization. Linear stability analysis, together with linear-wave validation, clarifies the roles of these parameters in controlling numerical dissipation and dispersion, which is then examined in more complicated numerical examples. It is demonstrated that the reformulated SLBM preserves the second-order accuracy, improves the dispersion-dissipation performance, remains stable in under-resolved cases, and resolves fine vortex structures on relatively coarse grids. Thus, the proposed method combines improved numerical properties with the simplicity of SLBM, offering a high-fidelity and stable scheme for incompressible flow simulations.
Source: Revisit the simplified lattice Boltzmann method: dissipation, dispersion and stability