| Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2977 - 3006 | |
| DOI | https://doi.org/10.1051/m2an/2023066 | |
| Published online | 25 September 2023 | |
Time-explicit hybrid high-order method for the nonlinear acoustic wave equation
1
Université Paris-Saclay, CEA, Service d’études mécaniques et thermiques, 91191 Gif-sur-Yvette, France
2
CERMICS, Ecole des Ponts, 77455 Marne-la-Vallée 2, France
3
INRIA, 2 rue Simone Iff, 75589 Paris, France
* Corresponding author: morgane.steins@enpc.fr
Received:
27
January
2023
Accepted:
2
August
2023
We devise a fully explicit scheme for the nonlinear acoustic wave equation in its second-order formulation in time, using the HHO method for space discretization and the leapfrog scheme for time integration. The key idea for the explicitation is an iterative procedure to approximate at each time step the static nonlinear coupling between the cell and face unknowns. This procedure is based on a splitting of the HHO stabilization operator and, in the linear case, is proved to converge for a large enough weight of the stabilization uniformly in the mesh size. Increasing the stabilization weight turns out to have a moderate impact on the CFL condition. The numerical experiments demonstrate the computational efficiency of the splitting procedure compared to a semi-implicit scheme for the static coupling between cell and face unknowns.
Mathematics Subject Classification: 65M22 / 65M60 / 35L05 / 74J30 / 65F10
Key words: Hybrid high-order methods / wave equation / explicit time scheme / operator splitting
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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