TY - JOUR
T1 - Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations
AU - Yu , Yuan
AU - Qin , Zuojian
AU - Chen , Siwei
AU - Shu , Shi
AU - Yuan , Haizhuan
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 489
EP - 516
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2024-0203
UR - https://global-sci.org/intro/article_detail/aamm/23731.html
KW - Regularized lattice Boltzmann, two-relaxation-time, high-Reynolds number, creeping flow, numerical slip.
AB - <p style="text-align: justify;">In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows, which
demonstrates superior stability and accuracy over existing models such as the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models. In this model,
a free relaxation parameter, $\tau_{s,2},$ is employed to relax the regularized non-equilibrium
third-order terms. Chapman-Enskog analysis reveals that our model can accurately
recover the Navier-Stokes equations. Theoretical analysis and numerical experiments
both confirm the model’s ability to eliminate non-physical numerical slip associated
with the half-way bounce-back scheme. Our simulations of the double shear layer
problem and Taylor-Green vortex flow exhibit pronounced advantages in terms of stability and accuracy, even under super-high Reynolds numbers as high as ${\rm Re}=10^7.$ Additionally, the simulation of creeping flow around a square cylinder showcases the
model’s precision in computing ultra-low Reynolds numbers down to ${\rm Re}=10^{−7}.$ This
robust capability confirms the proposed model as a highly effective and adaptable tool
in computational fluid dynamics.</p>