Implicit discretization of Lagrangian gas dynamics

Alexiane Plessier (1, 2) , Stéphane del Pino (1, 3) , Bruno Després (1, 4)

1 DAM/DIF - DAM Île-de-France
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 LIHPC - Laboratoire en Informatique Haute Performance pour le Calcul et la simulation
4 IUF - Institut universitaire de France

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.

Keywords: Implicit finite volume scheme; Lagrangian formalism; Entropy stability; Convex analysis

Domains: Mathematics [math]

Alexiane Plessier, Stéphane del Pino, Bruno Després. Implicit discretization of Lagrangian gas dynamics. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (2), pp.717-743. ⟨10.1051/m2an/2022102⟩. ⟨hal-04048418v4⟩