A 3D kinetic study of relaxation processes caused by the electron beam propagation in high-temperature plasma was carried out. This problem has two different spatial scales: the plasma Debye length and the beam-plasma interaction wavelength, that is, some 10 or 100 times larger, thus one needs high-performance computing to observe the two lengths at once. The mathematical model is built on the basis of the Particle-in-Cell (PIC) method and, also, the finite-difference kinetic approach is employed. The question to be answered within the model is how the numerical (model) collisions affect the course of interaction. To answer this question, the Bolzmann equation is solved with the Bhatnagar-Gross-Krook (BGK) collision term. The result is the following: the initial two-stream velocity distribution becomes uniform due to the role of collisions in the BGK equation in the same way as it happens in the collisionless PIC model with a coarse grid. This means that a coarse grid imposes collisions that are to be taken into account.