Optimal transport on gas networks

TL;DR

This paper introduces a novel approach to modeling gas networks using optimal transport theory, specifically developing a generalized Wasserstein metric and gradient flows on metric graphs with Euler equations.

Contribution

It presents a new framework for gas network modeling based on optimal transport, including a generalized p-Wasserstein metric and gradient flows for the case p=3.

Findings

Development of a generalized p-Wasserstein metric for gas networks

Derivation of p-Wasserstein gradient flows on metric graphs

Application to the non-standard case p=3

Abstract

This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized $p$-Wasserstein metric in a dynamic formulation is introduced and utilized to derive $p$-Wasserstein gradient flows, specifically focusing on the non-standard case $p = 3$.