Conservative solution methods for extended Boltzmann equations (Q2778010)

The present paper proposes some numerical methods for solving a class of extended semi-continuous kinetic Boltzmann equations which take into account both collision excitation and collision de-excitation processes together with the interaction with monochromatic photons. Conservation properties and H-theorem are obtained. The corresponding Legendre polynomial multigroup equations are derived as well as the truncated moment equations. As illustrative examples, these methods are applied to high frequency acoustic waves occuring in degenerate four wave mixing experiments and the propagation of a hot spot within a cold medium. The last section presents multigroup approaches to the extended linear Boltzmann equation governing the evolution of charged structureless particles scattering inelastically with heavy field particles. The concluding result is the formulation of a multigroup approach which is consistent with the non-linear Boltzmann equation.