Hyperbolic discretization of simplified Euler equation via Riemann invariants

Abstract

We are interested in numerical schemes for the simulation of large scale gas networks. Gas transport is described by a simplified Euler equation with a general equation of state for the pressure, including in particular the isentropic as well as the isothermal case. The numerical scheme is based on transformation of conservative variables in Riemann invariants and its corresponding numerical discretization. A novelty of the proposed method is the possibility to allow for an efficient discretization of the boundary and coupling conditions at nodal points of the network, as well as obtaining well balanced schemes. The proposed discretization is analysed in view of its property to correctly recover steady states as well as to resolve possible analytic solutions. Comparisons with existing methods are presented.