A multiple-relaxation time (MRT) lattice Boltzmann model (LBM) on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LBM model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the Navier-Stokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the 2D decaying Taylor-Green vortex flow and the liddriven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model [Bouzidi et al., J. Comp. Phys. 172 (2001) 704-717] are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.

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