This paper is concerned with a set of novel coupling conditions for the 3x3 one-dimensional Euler system with source terms at a junction of pipes with possibly different cross-sectional areas. Beside conservation of mass, we require the equality of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that
belong to pipes with incoming flow. These conditions ensure energy as well as entropy conservation at the junction. We prove the existence and uniqueness of solutions to the generalised Riemann problem at a junction in the neighbourhood of constant stationary states which belong to the subsonic region. This provides the basis for the well-posedness of the homogeneous and inhomogeneous Cauchy problems for initial data with sufficiently small total variation.
This paper is concerned with coupling conditions at junctions for transport
models which differ in their fidelity to describe transient flow in gas pipelines.
It also includes the integration of compressors between two pipes with possibly
different models. A hierarchy of three one-dimensional gas transport models is
built through the 3 × 3 polytropic Euler equations, the 2 × 2 isentropic Euler
equations and a simplified version of it for small velocities. To ensure entropy
preservation, we make use of the novel entropy-preserving coupling conditions
recently proposed by Lang and Mindt [Netw. Heterog. Media, 13:177-190,
2018] and require the equality of the total enthalpy at the junction and that
the specific entropy for pipes with outgoing flow equals the convex combination
of all entropies that belong to pipes with incoming flow. We prove the existence
and uniqueness of solutions to generalised Riemann problems at a junction in
the neighbourhood of constant coupling functions and stationary states which
belong to the subsonic region. This provides the basis for the well-posedness of
certain Cauchy problems for initial data with sufficiently small total variation.
