In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac structures. The first novelty of the presented model is the inclusion of non-zero energy exchange through, and within, the spatial boundaries of the domain containing the fluid. The second novelty is that the port-Hamiltonian model is constructed as the interconnection of a small set of building blocks of open energetic subsystems. Depending only on the choice of subsystems one composes and their energy-aware interconnection, the geometric description of a wide range of fluid dynamical systems can be achieved. The constructed port-Hamiltonian models include a number of inviscid fluid dynamical systems with variable boundary conditions. Namely, compressible isentropic flow, compressible adiabatic flow, and incompressible flow. Furthermore, all the derived fluid flow models are valid covariantly and globally on n-dimensional Riemannian manifolds using differential geometric tools of exterior calculus.

在这个由两部分组成的论文中，我们提出了一个系统的过程，以将关于Lie-Poisson结构的黎曼流形上的理想无粘性流体流的已知哈密顿模型扩展为根据Stokes-Dirac结构的哈密尔顿模型。所提出的模型的第一个新颖之处在于，它通过包含流体的区域的空间边界以及在空间边界内进行了非零能量交换。第二个新奇之处在于，将港口-哈密尔顿模型构建为开放式能量子系统的一小部分构建块的互连。仅取决于组成子系统的选择及其能量感知的互连，就可以实现各种流体动力学系统的几何描述。构造的哈密尔顿港模型包括许多具有可变边界条件的无粘性流体动力学系统。即，可压缩的等熵流，可压缩的绝热流和不可压缩的流。此外，使用外部演算的微分几何工具，所有导出的流体流动模型在n维黎曼流形上均可以协变且全局有效。