Structure‐preserving methods for a coupled port‐Hamiltonian system of compressible non‐isothermal fluid flow

Abstract

AbstractThe port‐Hamiltonian (pH) formulation of partial‐differential equations and their numerical treatment have been elaborately studied lately. One advantage of pH‐systems is that fundamental physical properties, like energy dissipation and mass conservation, are encoded in the system structure. Therefore, structure‐preservation is most important during all stages of approximation and system coupling. In this context we consider the non‐isothermal flow of a compressible fluid through a network of pipes. Based on a pH‐formulation of Euler‐type equations on one pipe, we introduce coupling conditions, through which we can realize energy, mass and entropy conservation at the coupling nodes and thus, preserve the pH‐structure. We implement them through an input‐output‐coupling using the flow and effort variables of the boundary port. Thus, we can make use of the structure‐preserving model and complexity reduction techniques for the single pipe. This procedure becomes even more important for network simulations, as here, we deal with high dimensional and highly non‐linear dynamical systems. We explain the extension from a single pipe to a network and numerical examples are shown to support our findings.