Conduction-Diffusion in N-Dimensional settings as irreversible port-Hamiltonian systems

TL;DR

This paper generalizes the modeling of conduction and diffusion processes in N-dimensional systems within an irreversible port-Hamiltonian framework, ensuring thermodynamic consistency and energy balance for complex multi-physical phenomena.

Contribution

It extends 1D IPHS formulations to N-dimensional boundary-controlled systems, unifying conduction and diffusion in a thermodynamically consistent structure.

Findings

Unified modeling of conduction and diffusion in N dimensions.

Preservation of energy balance and entropy production.

Foundation for structure-preserving numerical schemes.

Abstract

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.