# Coupling conditions for isothermal gas flow and applications to valves

## TL;DR

This paper models isothermal gas flow through pipes with electronic valves, introducing a new notion of coupling solutions that captures valve behaviors and analyzing their properties and conditions for stability and coherence.

## Contribution

It introduces a novel concept of coupling solutions for valve-influenced gas flow and provides explicit conditions ensuring key properties like coherence and continuity.

## Key findings

- New notion of coherence related to valve behavior
- Explicit conditions for stability and invariance
- Model extension potential to various valve types

## Abstract

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves.