论文标题
理想流体流的哈米尔顿港建模：第一部分。基础和动能
Port-Hamiltonian Modeling of Ideal Fluid Flow: Part I. Foundations and Kinetic Energy
论文作者
论文摘要
在这两部分论文中，我们提出了一个系统的程序，以将已知的Hamiltonian模型扩展到利马尼亚歧管上的理想无Inviscid流体流量，该模型就lie-poisson结构而言，就stokes-dirac结构而言。提出的模型的第一个新颖性是通过包含流体的域的空间边界包含非零的能量交换。第二个新颖性是，哈米尔顿港模型被构造为一小部分开放式能量子系统的构建块的互连。仅取决于一个组成的子系统及其能源感知的互连，可以实现多种流体动力学系统的几何描述。构建的 - 哈米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。也就是说，可压缩的等递流，可压缩的绝热流和不可压缩的流动。此外，所有派生的流体流模型使用外部演算的差分几何工具在N维riemannian歧管上都是有效的协变量和全球有效的。
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.
