The simulation of a stationary fluid flow past an obstacle by the lattice Boltzmann method (LBM) in two dimensions is discussed. The combination of second-order expressions for far-field boundary conditions and a suitable treatment of the no-slip boundary condition at the obstacle surface with the nested grid-refinement technique can be applied to the LBM, resulting in a highly efficient method for the treatment of exterior flows. Furthermore, via replacing the nested time stepping by local time stepping, the resolution process can be substantially accelerated. A highly accurate drag coefficient was used to make an error assessment for various no-slip boundary conditions imposed on the obstacle surface. The analysis showed that the equilibrium method for treating the no-slip conditions is superior to halfway bounce-back and full-way bounce-back no-slip conditions when the relaxation time tau=1 . Also a tau -dependence test was made to evaluate the performance of different methods in the treatment of the no-slip boundary conditions.