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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2023

Implicit discretization of Lagrangian gas dynamics

Abstract

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.
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Dates and versions

hal-04048418 , version 1 (12-07-2021)
hal-04048418 , version 2 (01-06-2022)
hal-04048418 , version 3 (02-11-2022)
hal-04048418 , version 4 (27-03-2023)

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Cite

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⟩
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