论文标题
关于网络上非线性流问题的哈米尔顿港近似
On port-Hamiltonian approximation of a nonlinear flow problem on networks
论文作者
论文摘要
本文介绍了针对网络上一类非线性偏微分方程的结构保护近似的系统开发。该类包括由Brotropic Euler方程描述的气管网络系统。我们的方法一直以基于能量的建模概念（哈米尔顿港形式主义，传奇理论转换理论）为指导，这提供了方便且一般的推理路线。在对近似值的轻度假设下，可以显示质量的局部保护，能量结合以及港口 - 哈米尔顿港结构的遗传。我们的方法不仅限于常规空间离散化，而且还涵盖了通过不精确整合对非线性的复杂性降低。因此，它可以用作降低结构模型的基础。结合一个能量稳定的时间整合，我们以数值为例，使用Euler方程来证明该方法的适用性和良好稳定性。
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic Euler equations. Our approach is guided throughout by energy-based modeling concepts (port-Hamiltonian formalism, theory of Legendre transformation), which provide a convenient and general line of reasoning. Under mild assumptions on the approximation, local conservation of mass, an energy bound, and the inheritance of the port-Hamiltonian structure can be shown. Our approach is not limited to conventional space discretization but also covers complexity reduction of the nonlinearities by inexact integration. Thus, it can serve as a basis for structure-preserving model reduction. Combined with an energy stable time integration, we numerically demonstrate the applicability and good stability properties of the approach using the Euler equations as an example.
