GABURRO, Elena; ÖFFNER, Philipp; RICCHIUTO, Mario; TORLO, Davide

doi:10.1016/j.amc.2022.127644

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GABURRO, Elena
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

ÖFFNER, Philipp
Institut für Mathematik [Mainz]

RICCHIUTO, Mario
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

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Applied Mathematics and Computation. 2023-03, vol. 440, p. 127644

Elsevier

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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 machineprecision. 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.< Réduire

Mots clés en anglais

Hyperbolic Conservation Laws

ADER

Discontinuous Galerkin

Entropy Conservation/Stability

Structure Preserving

Relaxation Method

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High order entropy preserving ADER-DG schemes

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