  In this article, we present the structure-preserving discretization of linear
one-dimensional port-Hamiltonian (PH) systems of two conservation laws using
discontinuous Galerkin (DG) methods. We recall the DG discretization procedure
which is based on a subdivision of the computational domain, an elementwise
weak formulation with up to two integration by parts, and the interconnection
of the elements using several numerical fluxes. We present the interconnection
of the element models, which is power preserving in the case of conservative
(unstabilized) numerical fluxes, and we set up the resulting global PH state
space model. We discuss the properties of the obtained models, including the
effect of the flux stabilization parameter on the spectrum. Finally, we show
simulations with different parameters for a boundary controlled linear
hyperbolic system.
