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.

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

Domains: Numerical Analysis [math.NA]; Mathematics [math]

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