Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

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.