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High order entropy preserving ADER-DG schemes

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  • Gaburro, Elena
  • Öffner, Philipp
  • Ricchiuto, Mario
  • Torlo, Davide

Abstract

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.

Suggested Citation

  • Gaburro, Elena & Öffner, Philipp & Ricchiuto, Mario & Torlo, Davide, 2023. "High order entropy preserving ADER-DG schemes," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007160
    DOI: 10.1016/j.amc.2022.127644
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    References listed on IDEAS

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    1. Gassner, Gregor J. & Winters, Andrew R. & Kopriva, David A., 2016. "A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 291-308.
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    Cited by:

    1. Ciallella, Mirco & Gaburro, Elena & Lorini, Marco & Ricchiuto, Mario, 2023. "Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    2. Han Veiga, Maria & Micalizzi, Lorenzo & Torlo, Davide, 2024. "On improving the efficiency of ADER methods," Applied Mathematics and Computation, Elsevier, vol. 466(C).

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