Preconditioners for hyperbolic systems are numerical artifices intended to accelerate the convergence path to a steady state. In addition, in some cases, the preconditioner can also be included in the artificial viscosity/upwinding terms in order to improve the accuracy of the steady state solution. For time dependent problems we use a dual time stepping approach; and therefore the preconditioner affects the convergence rate and accuracy of the subiterations at each physical time step. We consider two types of local preconditioners that couple the governing equations at a node point: Jacobi and low-speed preconditioning. We consider their effectiveness for both steady state and time dependent problems with regard to the convergence rate and the numerical accuracy. We also consider the effect of the far field boundary conditions on both steady state and time dependent problems.