The recent advances about the construction of a Trefftz Discontinuous Galerkin (TDG) method to a class of Friedrichs systems coming from linear transport with relaxation are presented in a comprehensive setting. Application to the 2D P N model are discussed , together with the derivation of new high order convergence estimates and new numerical results for the P 1 and P 3 models. More numerical results in dimension 2 illustrate the theoretical properties.