A relaxation scheme for the equations of isentropic gas dynamics on a network with jump transmission conditions

TL;DR

This paper introduces a new relaxation-based numerical scheme for simulating isentropic gas dynamics on networks, effectively handling junction conditions and both subsonic and supersonic flows, with proven consistency and good performance.

Contribution

A novel relaxation scheme for Euler equations on networks that manages jump transmission conditions and works across flow regimes, with proven consistency and demonstrated effectiveness.

Findings

The scheme accurately approximates gas dynamics on networks.

It handles both subsonic and supersonic flow regimes.

Numerical tests show superior performance compared to existing solvers.

Abstract

In this paper we propose a new numerical scheme of relaxation type to approximate the Euler equations of isentropic gas dynamics on the arcs of a network. At the junction mass conservation and a jump transmission condition on the density are given, and a new solver is introduced to deal with both subsonic and supersonic cases. Consistency properties of the solver are proven and numerical tests are displayed to show its good performance also with respect to other possible solvers.