Implicit discretization of Lagrangian gas dynamics

A. Plessier (1, 2) , S. del Pino (1, 3) , B. Després (2, 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.

Mots clés: Implicit Finite Volume Scheme; Lagrangian Formalism; Entropy Stability; Convex Analysis

Domaines: Analyse numérique [math.NA]; Mathématiques [math]

A. Plessier, S. del Pino, B. Després. Implicit discretization of Lagrangian gas dynamics. 2021. ⟨hal-04048418v1⟩