Exergetic Port-Hamiltonian Systems: Navier-Stokes-Fourier Fluid

TL;DR

This paper introduces a modular modeling language combining bond graphs and port-Hamiltonian semantics to represent thermodynamic systems, demonstrated on a Navier-Stokes-Fourier fluid example.

Contribution

It presents a novel formal language for hierarchical and modular modeling of thermodynamic systems with thermodynamic laws embedded in the semantics.

Findings

Successfully models Navier-Stokes-Fourier fluid as an interconnected system

Provides a formal language accessible to humans and computers

Demonstrates modular and hierarchical specification of complex thermodynamic systems

Abstract

The Exergetic Port-Hamiltonian Systems modeling language combines a graphical syntax inspired by bond graphs with a port-Hamiltonian semantics akin to the GENERIC formalism. The syntax enables the modular and hierarchical specification of the composition pattern of lumped and distributed-parameter models. The semantics reflects the first and second law of thermodynamics as structural properties. Interconnected and hierarchically defined models of multiphysical thermodynamic systems can thus be expressed in a formal language accessible to humans and computers alike. We discuss a composed model of the Navier-Stokes-Fourier fluid on a fixed spatial domain as an example of an open distributed-parameter system. At the top level, the system comprises five subsystems which model kinetic energy storage, internal energy storage, thermal conduction, bulk viscosity, and shear viscosity.