| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 717 - 743 | |
| DOI | https://doi.org/10.1051/m2an/2022102 | |
| Published online | 27 March 2023 | |
Implicit discretization of Lagrangian gas dynamics
1
CEA, DAM, DIF, 91297 Arpajon, France
2
LJLL (UMR 7598) - Laboratoire Jacques Louis Lions, Paris, France
3
Université Paris-Saclay, Laboratoire en Informatique Haute Performance pour le Calcul et la simulation, Gif-sur-Yvette, France
4
IUF - Institut Universitaire de France, Paris, France
* Corresponding author: alexianesandra@gmail.com
Received:
1
June
2022
Accepted:
16
December
2022
We construct an original framework based on convex analysis to prove the existence and uniqueness of a solution to a class of implicit numerical schemes. We propose an application of this general framework in the case of a new non linear implicit scheme for the 1D Lagrangian gas dynamics equations. We provide numerical illustrations that corroborate our proof of unconditional stability for this non linear implicit scheme.
Mathematics Subject Classification: 65C20 / 65M12 / 65M12
Key words: Implicit finite volume scheme / Lagrangian formalism / Entropy stability / Convex analysis
© The authors. Published by EDP Sciences, SMAI 2023
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