Exergetic Port-Hamiltonian Systems: A compositional electro-magneto hydrodynamics model

Computational fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing computational models for complex coupled systems can be challenging and time-consuming. In particular, ensuring the consistent integration of models from diverse physical domains requires meticulous attention. Even if the coupling of specialized simulation tools based on different formalisms were practically feasible, the growing demand to combine first-principles-based modeling with scientific machine learning necessitates an integrated high-level approach to model specification. Considering the example of electro-magneto hydrodynamics (on a fixed spatial domain and with linear polarization and magnetization), this article demonstrates how relatively complex models can be hierarchically composed from simpler parts by means of a formal language for multiphysics modeling. The Exergetic Port-Hamiltonian Systems (EPHS) modeling language features a simple graphical syntax for expressing the energy-based interconnection of subsystems. This reduces cognitive load and facilitates communication, especially in multidisciplinary environments. As the example demonstrates, existing models can be easily integrated as subsystems of new models. Specifically, the ideal fluid model is used as a subsystem of the Navier-Stokes-Fourier fluid model, which in turn is used as a subsystem of the electro-magneto hydrodynamics model. The compositional approach makes it nearly trivial to encapsulate, reuse, and swap out (parts of) models. Moreover, structural properties of EPHS models guarantee fundamental properties of thermodynamic systems, such as conservation of energy, non-negative entropy production, and Onsager reciprocal relations.