Hyperbolic Discretization via Riemann Invariants

Abstract: We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative variables in Riemann invariants and its corresponding numerical dsicretization. A particular, novelty of the proposed method is the possbility to allow for an efficient discretization of the boundary and coupling conditions at nodal points of the network. The original 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 show the advantage of the novel method.