# Entropy-Preserving Coupling of Hierarchical Gas Models

## TL;DR

This paper develops entropy-preserving coupling conditions for hierarchical gas flow models at pipeline junctions, ensuring well-posedness and solution uniqueness for complex transient flow scenarios.

## Contribution

It introduces a novel entropy-preserving coupling framework for hierarchical gas models, including compressors, with proven existence and uniqueness of solutions.

## Key findings

- Existence and uniqueness of solutions at junctions.
- Well-posedness of Cauchy problems with small total variation.
- Framework applicable to models with compressors and different fidelities.

## Abstract

This paper is concerned with coupling conditions at junctions for transport models which differ in their fidelity to describe transient flow in gas pipelines. It also includes the integration of compressors between two pipes with possibly different models. A hierarchy of three one-dimensional gas transport models is built through the 3x3 polytropic Euler equations, the 2x2 isentropic Euler equations and a simplified version of it for small velocities. To ensure entropy preservation, we make use of the novel entropy-preserving coupling conditions recently proposed by Lang and Mindt [Netw. Heterog. Media, 13:177-190, 2018] and require the continuity of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that belong to pipes with incoming flow. We prove the existence and uniqueness of solutions to generalised Riemann problems at a junction in the neighbourhood of constant coupling functions and stationary states which belong to the subsonic region. This provides the basis for the well-posedness of certain Cauchy problems for initial data with sufficiently small total variation.