Extended-Regularized Lattice Boltzmann Method

Abstract

The Lattice Boltzmann Method (LBM) is widely used for simulating fluid dynamics due to its flexibility and computational efficiency. However, the standard BGK collision model suffers from numerical instabilities, particularly in high Reynolds number flows. The Regularized Lattice Boltzmann Method (RLBM) improves stability by filtering out non-hydrodynamic moment. In this work, we propose an extension of RLBM, which introduces a second relaxation time to further control high-order moments without compromising computational simplicity. Through numericalsimulations, including the Taylor-Green vortex and a double shear layer test case, we demonstrate that our extended method significantly enhances numerical stability while maintaining accuracy. Our results suggest that tuning the relaxation time of non-hydrodynamic moments allows simulations at higher Reynolds numbers with improved robustness.