Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Ottinger, Phys. Rev. Lett. 94, 080602 (2005)]-the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin's artificial compressibility method. A comparison of the two methods for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers shows that the results from both methods are in good agreement with each other. However, in the transient flow, it is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, unlike the artificial compressibility method.