Structure preserving spatial discretization of 1D convection-diffusion port-Hamiltonian systems

Convection-diffusion is a physical phenomenon that appears in a multitude of dynamical systems, e.g. vibrating string with damping or chemical and thermal systems. This paper focuses on a structure preserving spatial discretization scheme of a general dynamical system with convection and diffusion in the port-Hamiltonian framework. The preservation of the port-Hamiltonian structure ensures that specific properties, such as passivity, of the infinite dimensional system are preserved.