Relaxation Schemes for Nonlinear Kinetic Equations

A class of numerical schemes for nonlinear kinetic equations of Boltzmann type is described. Following Wild's approach, the solution is represented as a power series with parameter depending exponentially on the Knudsen number. This permits us to derive accurate and stable time discretizations for all ranges of the mean free path. These schemes preserve the main physical properties: positivity, conservation of mass, momentum, and energy. Moreover, for some particular models, the entropy property is also shown to hold.