The time-dependent method&LU-SGS implicit scheme has been used to solve 2D compressible Navier-Stokes equations which are preconditioned and simulate the driven cavity flow field at different low Mach numbers and different Reynold numbers. To apply the time-dependent method to simulate the flow field at low speeds validly and accelerate the convergence rates, a matrix called preconditioning matrix has multiplied the time-derivative terms of Navier-Stokes equations. This is known as preconditioning. Convergence rates are accelerated for a certainty, while providing solutions are identical to those obtained without preconditioning methods. The results are compared with available data.