We performed kinetic Vlasov simulations of the plasma-wall transition for a low-pressure argon discharge without external magnetic fields, using the same plasma parameters as in the experiments of Claire et al. [Phys. Plasmas 13, 062103 (2006)]. Experimentally, it was found that the ion velocity distribution function is highly asymmetric in the presheath, but, surprisingly, becomes again close to Maxwellian inside the sheath. Here, we show that this "thermalization" can be explained by purely collisionless effects that are akin to the velocity bunching phenomenon observed in charged particles beams. Such collisionless thermalization is also observed in the presheath region close to the sheath entrance, although it is much weaker there and in practice probably swamped by collisional processes (standard or enhanced by instabilities). V C 2015 AIP Publishing LLC.