The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes into play as it has several advantages, e.g., physical properties are encoded in the system structure and systems running on different time scales can be coupled easily. Additionally, pH systems coupled by energy-preserving conditions are still pH. Furthermore, in the energy transition hydrogen becomes an important player and unlike in natural gas, its temperature-dependence is of importance. Thus, we introduce an infinite dimensional pH formulation of the compressible non-isothermal Euler equations to model flow with temperature-dependence. We set up the underlying Stokes-Dirac structure and deduce the boundary port variables. We introduce coupling conditions into our pH formulation, such that the whole network system is pH itself. This is achieved by using energy-preserving coupling conditions, i.e., mass conservation and equality of total enthalpy, at the coupling nodes. Furthermore, to close the system a third coupling condition is needed. Here, equality of the outgoing entropy at coupling nodes is used and included into our systems in a structure-preserving way. Following that, we adapt the structure-preserving aproximation methods from the isothermal to the non-isothermal case. Academic numerical examples will support our analytical findings.

翻译：可再生能源的高波动性要求更高的能源效率。因此，尽管不同物理系统运行于不同时间尺度，仍需对其实现高效耦合。此时，端口-哈密顿（port-Hamiltonian, pH）建模框架因其多重优势而发挥作用，例如物理特性被编码于系统结构中，且不同时间尺度的系统可被便捷耦合。此外，通过能量守恒条件耦合的pH系统仍保持pH特性。在能源转型中，氢气正成为重要角色，与天然气不同，其温度依赖性至关重要。因此，我们引入可压缩非等温欧拉方程的无穷维pH表述以模拟具有温度依赖性的流动。我们构建了底层斯托克斯-狄拉克结构，并推导出边界端口变量。我们在pH表述中引入耦合条件，使得整个网络系统本身成为pH系统。这是通过在耦合节点处采用能量守恒耦合条件（即质量守恒与总焓相等）实现的。此外，为封闭系统需要第三个耦合条件。此处采用耦合节点处输出熵相等条件，并以保持结构的方式将其纳入系统。随后，我们将保持结构的逼近方法从等温情形推广至非等温情形。学术数值算例将佐证我们的理论分析结果。