Statistical particle in cell for solving the phonon Boltzmann equation

The propagation of heat in a crystal is considered as a process of transport of phonons – quasi-particles with quasi-momentum and energy. The Boltzmann kinetic equation is constructed for the phonon’s distribution function in the phase space. The scattering of phonons is modeled in the approximation of the time of relaxation of their distribution to the equilibrium state. The numerical algorithm for solving the kinetic equation is based on the statistical method of particles, which combines the solution of the phonons motion equations with stochastic modeling of their creation and annihilation. The results of the numerical solution of the problems of temperature relaxation in a crystal during heating of its surface and energy release in the volume are considered.