High order entropy preserving ADER-DG schemes

Elena Gaburro (1) , Philipp Öffner (2) , Mario Ricchiuto (1) , Davide Torlo (3)

1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
2 Institut für Mathematik [Mainz]
3 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method with entropy correction terms that balance the entropy production in space, inspired by the work of Abgrall. Whereas for the time-discretization we apply the relaxation approach introduced by Ketcheson that allows to modify the timestep to preserve the entropy to machine precision. Up to our knowledge, it is the first time that a provable fully discrete entropy preserving ADER-DG scheme is constructed. We verify our theoretical results with various numerical simulations.

Mots clés: Hyperbolic Conservation Laws; ADER; Discontinuous Galerkin; Entropy Conservation/Stability; Structure Preserving; Relaxation Method

Domaines: Mathématiques [math]

Elena Gaburro, Philipp Öffner, Mario Ricchiuto, Davide Torlo. High order entropy preserving ADER-DG schemes. Applied Mathematics and Computation, 2023, 440, pp.127644. ⟨10.1016/j.amc.2022.127644⟩. ⟨hal-03850196⟩