Rarefied gas flows around a NACA 0012 airfoil are simulated using both particle and continuum approaches. Three different conditions are considered: supersonic, transonic, and low subsonic. In all three cases, the continuum approach solves the Navier-Stokes equations with a slip boundary condition on the airfoil surface. For the supersonic and transonic cases, the particle method employed is the direct simulation Monte Carlo method. Because of problems with this method at the low subsonic condition, caused by excessive statistical fluctuations, a new particle method called the information preservation technique is applied. The computed density and velocity flowfields are compared with experimental data and found to be in generally good agreement. Some interesting features in the surface pressure distributions along the airfoil are found for these low-Reynolds-number flows.