Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows, whichdemonstrates 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, $τ_{s,2},$ is employed to relax the regularized non-equilibriumthird-order terms. Chapman-Enskog analysis reveals that our model can accuratelyrecover the Navier-Stokes equations. Theoretical analysis and numerical experimentsboth confirm the model’s ability to eliminate non-physical numerical slip associatedwith the half-way bounce-back scheme. Our simulations of the double shear layerproblem 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 themodel’s precision in computing ultra-low Reynolds numbers down to ${\rm Re}=10^{−7}.$ Thisrobust capability confirms the proposed model as a highly effective and adaptable toolin computational fluid dynamics.