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 an (electro-)magneto hydrodynamics model. The energy-based, compositional approach simplifies understanding complex models, and it makes it easy to encapsulate, reuse, and replace (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.

翻译：流体动力学在能源系统、电子冷却和生物医学工程等多种多物理场应用中起着至关重要的作用。为复杂的耦合系统开发模型可能具有挑战性且耗时。特别是，确保来自不同物理领域的模型能够一致地集成需要细致的关注。本文以（电）磁流体动力学（在固定空间域中，并考虑线性极化和磁化）为例，展示了如何通过一种用于多物理场建模的形式化语言，从较简单的部分组合出相对复杂的模型。Exergetic Port-Hamiltonian Systems (EPHS) 建模语言具有简单的图形语法，用于表达子系统间基于能量的互连。这降低了认知负担，并促进了交流，尤其是在多学科环境中。如示例所示，现有模型可以轻松地作为新模型的子系统进行集成。具体而言，理想流体模型被用作 Navier-Stokes-Fourier 流体模型的子系统，而后者又被重新用作（电）磁流体动力学模型的子系统。这种基于能量的组合方法简化了对复杂模型的理解，并使模型的（部分）封装、重用和替换变得容易。此外，EPHS 模型的结构特性保证了热力学系统的基本性质，如能量守恒、非负熵产生以及 Onsager 倒易关系。