Implicit discretization of Lagrangian gas dynamics

A. Plessier (1, 2) , S. del Pino (3, 2) , B. Després (1, 4)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 DAM/DIF - DAM Île-de-France
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]; Numerical Analysis [math.NA]; Mathematics [math]

A. Plessier, S. del Pino, B. Després. Implicit discretization of Lagrangian gas dynamics. 2022. ⟨cea-03284467v3⟩