A multicell approximation to the Boltzmann equation for bimolecular chemical reactions

A new numerical method for solving the Boltzmann equation describing chemical reactions in the gas phase is introduced. The method aims at governing also strong anisotropies of the distribution function of some species, which might be beyond the range of applicability of the PN-approximation. The developed multicell approximation is based simply on a partition of the phase space of each molecule species into a large number of cells. The corresponding distribution function is assumed to be constant inside a cell. By integrating the Boltzmann equations separately over each cell, a completely determined system of coupled ordinary differential equations is obtained. The system implicitly guarantees particle conservation, whereas total momentum and energy conservation is reproduced only in the limit of vanishing cell size. In this first approach, the method is tested versus problems which are one-dimensional in velocity space.