Rarefied Gas Dynamics A stream of gas molecules meets a cylinder. When the gas is dense (low Knudsen number) molecules collide constantly, act as a continuous fluid, and pile into a curved shock ahead of the body. Thin the gas out and collisions become rare: molecules just fly straight, hit the body one at a time, and there is no shock at all — only a shadow. The journey: the Knudsen number Kn = λ/D compares the mean free path to the body size. Kn → 0 gives Navier–Stokes; Kn → ∞ gives free-molecular flight. Here collisions are modelled by relaxing each molecule toward its neighbourhood’s average, at a rate set by the local density and 1/Kn.