  In this paper, we propose a new semi-Lagrangian scheme for the polyatomic
ellipsoidal BGK model. In order to avoid time step restrictions coming from
convection term and small Knudsen number, we combine a semi-Lagrangian approach
for the convection term with an implicit treatment for the relaxation term. We
show how to explicitly solve the implicit step, thus obtaining an efficient and
stable scheme for any Knudsen number. We also derive an explicit error estimate
on the convergence of the proposed scheme for every fixed value of the Knudsen
number.
