  In this article, we propose a new numerical model for computation of the
transport of electrons in a graphene device. The underlying quantum model for
graphene is a massless Dirac equation, whose eigenvalues display a conical
singularity responsible for non adiabatic transitions between the two modes. We
first derive a kinetic model which takes the form of two Boltzmann equations
coupled by a collision operator modeling the non-adiabatic transitions. This
collision term includes a Landau-Zener transfer term and a jump operator whose
presence is essential in order to ensure a good energy conservation during the
transitions. We propose an algorithmic realization of the semi-group solving
the kinetic model, by a particle method. We give analytic justification of the
model and propose a series of numerical experiments studying the influences of
the various sources of errors between the quantum and the kinetic models.
