Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach (Advances in Applied Mathematics and Mechanics, 2018)
Numerical instability may occur when simulating high Reynolds numberflows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT)model of the LBM can improve the accuracy and stability, but is still subject to numericalinstability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number). The viscosity counteracting approach proposed recentlyis a method of enhancing the stability of the LBM. However, its effectivenesswas only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paperaims to propose the viscosity counteracting approach for the multiple-relaxation-timemodel (MRT-LBM) and analyze its numerical characteristics. The verification isconducted by simulating some benchmark cases: the two-dimensional (2D) lid-drivencavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional(3D) rectangular jet. Qualitative and Quantitative comparisons show thatthe viscosity counteracting approach for the MRT-LBM has better accuracy and stabilitythan that for the SRT-LBM.