Authors

Markus Lohmayer, Michael Kraus, Sigrid Leyendecker

Abstract

Fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing 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. 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 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, an ideal fluid model is used as a subsystem of a Navier-Stokes-Fourier fluid model, which in turn is reused as a subsystem of a magneto-hydrodynamics model. The energy-based, compositional approach simplifies understanding complex models, and it makes it easy to encapsulate, reuse, and replace their constituents. Moreover, structural properties of EPHS guarantee fundamental properties of thermodynamic systems, such as conservation of energy, non-negative entropy production, and Onsager reciprocal relations.

Keywords

bond graphs, compositionality, exterior calculus, generic formalism, graphical syntax, magnetohydrodynamics, metriplectic systems, modeling language, multiphysics, navier-stokes-fourier fluid, nonequilibrium thermodynamics, port-hamiltonian systems, undirected wiring diagrams

Citation

  • Journal: Communications in Nonlinear Science and Numerical Simulation
  • Year: 2026
  • Volume: 152
  • Issue:
  • Pages: 109384
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.cnsns.2025.109384

BibTeX

@article{Lohmayer_2026,
  title={{Energy-based, geometric, and compositional formulation of fluid and plasma models}},
  volume={152},
  ISSN={1007-5704},
  DOI={10.1016/j.cnsns.2025.109384},
  journal={Communications in Nonlinear Science and Numerical Simulation},
  publisher={Elsevier BV},
  author={Lohmayer, Markus and Kraus, Michael and Leyendecker, Sigrid},
  year={2026},
  pages={109384}
}

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References