Coupling conditions for gas networks governed by the isothermal Euler equations

Abstract

We investigate coupling conditions for gas transport in networks where the governing equations are the isothermal Euler equations. We discuss intersections of pipes by considering solutions to Riemann problems. We introduce additional assumptions to obtain a solution near the intersection and we present numerical results for sample networks.

ADER schemes and high order coupling on networks of hyperbolic conservation laws

“…(6) or (7), a classical Riemann problem is obtained. A detailed analysis of the Riemann problem at a junction of p-systems can be found in [29].…”

“…The length of the edges is L = 1 and as coupling conditions we use the equal height conditions (6). As numerical method on the edges we use the ADER scheme as described in [18].…”

“…Networks of hyperbolic conservation laws occur in many applications such as the human circulatory system [1,2,3,4], gas pipelines [5,6,7], water [8,9,10,11] and road networks [12,13]. For all these applications accurate and stable numerical methods are needed.…”

“…Special attention has to be given to the coupling conditions. The direct solving of the coupling conditions only provides first order information, which can either be used directly by applying a Godunov scheme [6,23] or to fill corresponding ghost cells [9,24] at the boundary. A second order approach is studied in [25].…”

A domain decomposition method for conservation laws with discontinuous flux function

“…We present an alternative view on those problems by introducing a domain decomposition procedure [19,15,8]. Our approach is inspired from recent work on partial differential equation on network geometries, see for example [9,4,1], and therefore coupling conditions for the subdomains are similar to the coupling conditions at the vertices of a network model.…”