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.

翻译：计算流体动力学在多种多物理场应用中发挥着关键作用，包括能源系统、电子冷却和生物医学工程。为复杂耦合系统开发计算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。即使基于不同形式体系的专用仿真工具的耦合在实际中可行，将基于第一性原理的建模与科学机器学习相结合日益增长的需求，也要求一种集成的高层次模型规范方法。以电磁流体动力学（在固定空间域上，并具有线性极化和磁化）为例，本文展示了如何通过一种多物理场建模的形式化语言，从较简单的部分层次化地组合出相对复杂的模型。基于能量的端口哈密顿系统（EPHS）建模语言具有简单的图形语法，用于表达基于能量的子系统互连。这降低了认知负荷并促进了交流，特别是在多学科环境中。如示例所示，现有模型可以轻松地作为新模型的子系统集成。具体而言，理想流体模型被用作纳维-斯托克斯-傅里叶流体模型的子系统，而后者又被用作电磁流体动力学模型的子系统。这种组合式方法使得封装、重用和替换模型（的部分）变得几乎轻而易举。此外，EPHS模型的结构特性保证了热力学系统的基本性质，例如能量守恒、非负熵产生以及昂萨格倒易关系。