Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems
This provides a foundation for systematic modeling and control of complex multi-physical processes in fields like fluid dynamics, though it is incremental as it extends prior 1D work to N dimensions.
The paper tackles the problem of modeling conduction-diffusion phenomena in N-dimensional distributed systems by extending a 1D irreversible port-Hamiltonian formulation, resulting in a unified framework that preserves energy balance and characterizes entropy production correctly.
This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically consistent framework, we show that conduction and diffusion can be represented through a single coherent structure that preserves global energy balance and ensures a correct characterization of entropy production. The resulting formulation provides a foundation for the systematic modeling and control of complex multi-physical processes governed by coupled transport mechanisms in N dimensions. In the longer term, this framework opens the door to structure-preserving numerical schemes capable of enforcing thermodynamic principles directly at the discretized level.