Stability and asymptotic analysis for instationary gas transport via relative energy estimates

We consider the transport of gas in long pipes and pipeline networks for which the dynamics are dominated by friction at the pipe walls. The governing equations can be formulated as an abstract dissipative Hamiltonian system which allows us to derive perturbation bounds via relative energy estimates using a problem adapted nonlinear analysis. As particular consequences of these results, we are able to prove stability estimates with respect to initial conditions and model parameters and we conduct a quantitative asymptotic analysis in the high friction limit. Our results are established first for the flow in a single pipe and we then extend our analysis to pipe networks in the spirit of energy-based port-Hamiltonian modelling.

Automated summary

This article investigates the transportation of gas in long pipes and pipeline networks, where the dynamics are primarily influenced by friction at the pipe walls. By employing nonlinear analysis, the governing equations are formulated as an abstract dissipative Hamiltonian system, enabling us to derive perturbation bounds through relative energy estimates. Consequently, stability estimates with respect to initial conditions and model parameters are proven, and a quantitative asymptotic analysis is conducted in the high friction limit. Initially, the results are established for flow in a single pipe, and then the analysis is extended to pipe networks in the energy-based port-Hamiltonian modeling framework.