  We construct a lattice kinetic scheme to study electronic flow in graphene.
For this purpose, we first derive a basis of orthogonal polynomials, using as
weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later,
we use these polynomials to expand the respective distribution in a moving
frame, for both cases, undoped and doped graphene. In order to discretize the
Boltzmann equation and make feasible the numerical implementation, we reduce
the number of discrete points in momentum space to 18 by applying a Gaussian
quadrature, finding that the family of representative wave (2+1)-vectors, that
satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and
discrete model are validated by solving the Riemann problem, finding excellent
agreement with other numerical models. In addition, we have extended the
Riemann problem to the case of different dopings, finding that by increasing
the chemical potential, the electronic fluid behaves as if it increases its
effective viscosity.
