Abstract <p>Numerical solutions produced by the discrete velocity method as applied to nonstationary rarefied gas flow problems with discontinuous boundary conditions exhibit oscillations. This phenomenon is known as the “ray effect,” which is a significant obstacle to the numerical integration of kinetic equations in highly nonequilibrium regimes at low collision frequencies. In many cases, the oscillations of macroscopic parameters can be reduced by applying a global adaptive velocity mesh. The performance of this algorithm is demonstrated as applied to a two-dimensional evaporation problem related to the interaction of laser radiation with matter.</p>