  In this paper, we propose a novel two-relaxation-time regularized lattice
Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows.
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 (NSEs). Theoretical
analysis of the Poiseuille flow problem demonstrates that the slip velocity
magnitude in the proposed model is controlled by a magic parameter, which can
be entirely eliminated under specific values, consistent with the classical TRT
model. Our simulations of the double shear layer problem, Taylor-Green vortex
flow, and force-driven Poiseuille flow confirm that the stability and accuracy
of our model significantly surpass those of both the regularized lattice
Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high
Reynolds numbers as $Re=10^7$. Concurrently, the TRT-RLB model exhibits
superior performance in very high viscosity scenarios. The simulations of
creeping flow around a square cylinder demonstrates the model's capability to
accurately compute ultra-low Reynolds numbers as $Re=10^{-7}$. This study
establishes the TRT-RLB model as a flexible and robust tool in computational
fluid dynamics.
