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3 results on '"Implicit finite volume scheme"'

1. Implicit discretization of Lagrangian gas dynamics.

Author

Plessier, Alexiane, Del Pino, Stéphane, and Després, Bruno

Subjects
*GAS dynamics, *EQUATIONS, *ENTROPY
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. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Implicit discretization of Lagrangian gas dynamics

Author

Alexiane Plessier, Stéphane Del Pino, Bruno Després, DAM Île-de-France (DAM/DIF), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire en Informatique Haute Performance pour le Calcul et la simulation (LIHPC), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), CEA,DAM,DIF, and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)

Subjects
Convex analysis, Lagrangian formalism, [MATH]Mathematics [math], Implicit finite volume scheme, Entropy stability, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; 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.

Published
2023

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