553 RWTH Publication No: 788512        2020       
TITLE New Coupling Conditions for Isentropic Flow on Networks
AUTHORS Yannick Holle, Michael Herty, Michael Westdickenberg
ABSTRACT We introduce new coupling conditions for isentropic flow on net- works based on an artificial density at the junction. The new coupling condi- tions can be 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 prob- lem is globally in state space. Furthermore, non-increasing energy at the junc- tion and a maximum principle are proven. A numerical example is given in which the new conditions are the only known conditions leading to the physi- cally correct wave types. The approach generalizes to full gas dynamics.
DOI 10.3934/nhm.2020016