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

Abstract

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 by means of relative energy estimates. As particular consequences, we obtain stability with respect to initial conditions and model parameters and quantitative estimates in the high friction limit. Our results are established in detail for the flow in a single pipe and through the energy-based modelling they naturally generalize also to pipe networks.

References in corpus (4)

• A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws
• Relative entropy in diffusive relaxation
• Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
• From gas dynamics with large friction to gradient flows describing diffusion theories

Cited by in corpus (3)

• Optimal transport on gas networks
• Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions
• An Asymptotic-Preserving Scheme for Isentropic Flow in Pipe Networks