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In this article, we present the structure-preserving discretization of linearone-dimensional port-Hamiltonian (PH) systems of two conservation laws usingdiscontinuous Galerkin (DG) methods. We recall the DG discretization procedurewhich is based on a subdivision of the computational domain, an elementwiseweak formulation with up to two integration by parts, and the interconnectionof the elements using several numerical fluxes. We present the interconnectionof the element models, which is power preserving in the case of conservative(unstabilized) numerical fluxes, and we set up the resulting global PH statespace model. We discuss the properties of the obtained models, including theeffect of the flux stabilization parameter on the spectrum. Finally, we showsimulations with different parameters for a boundary controlled linearhyperbolic system.

Structure preserving discontinuous Galerkin approximation of one-dimensional port-Hamiltonian systems