No. 2020.06
New Coupling Conditions for Isentropic Flow on Networks
Y. Holle, M. Herty, and M. Westdickenberg
Subject: Hyperbolic conservation laws, networks, coupling condition, isentropic gas dynamics, kinetic model, maximum entropy dissipation
Abstract
We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling condition can be formally derived from a kinetic model by imposing a condition on energy dissipation. Existence and uniqueness of solutions to the generalized Riemann and Cauchy problem are proven. The result for the generalized Riemann problem is globally in state space. Furthermore, non-increasing energy at the junction and a maximum principle on the Riemann invariants are proven. Our approach generalizes to full gas dynamics.