507	RWTH Publication No: 804642        2020        IGPM507.pdf
TITLE	Well-balanced discontinuous Galerkin scheme for 2 × 2 hyperbolic balance law
AUTHORS	Yogiraj Mantri, Sebastian Noelle
ABSTRACT	The numerical solutions to nonlinear hyperbolic balance laws at (or near) steady state may develop spurious oscillations due to the imbalance between flux and source terms. In the present article, we study a high order well-balanced discontinuous Galerkin (DG) scheme for balance law with subsonic flow, which preserves equilibrium solutions of the flow exactly, and also provides non-oscillatory solutions for flow near equilibrium. The key technique is to reformulate the DG scheme in terms of global equilibrium variables which remain constant in space and time, and are obtained by rewriting the balance law in conservative form. We show that the proposed scheme is well-balanced and validate the scheme for various flows given by 2 × 2 hyperbolic balance law. We also extend the scheme to flows on networks, particularly to include the coupling conditions at nodes of the network.
KEYWORDS	well-balanced scheme, discontinuous Galerkin scheme, hyperbolic balance laws, flows on networks
DOI	10.1016/j.jcp.2020.110011
PUBLICATION	Journal of Computational Physics Volume 429, 15 March 2021