Nous cherchons une approximation numérique des solutions discontinues de type onde de choc d'un système hyperbolique non conservatif. Le système considéré est issue d'une modélisation simplifiée d'un écoulement bifluide. Les ondes de choc sont définies par l'introduction d'un tenseur de diffusion. Sur la base d'équations supplémentaires satisfaites par les solutions du système, nous proposons un schéma de type volume fini consistant avec la définition des solutions discontinues
We consider, for numerical approximations, a nonconservative hyperbolic system which arises when modeled a bifluid flow. We introduce a diffusion tensor to define the discontinuous shock wave solutions and we exhibit additional laws satisfied by the smooth solutions. Arguing the additional laws, we propose a numerical method shown to be consistant with the definition of discontinuous solutions.
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Christophe Berthon 1
@article{CRMATH_2002__335_12_1069_0,
author = {Christophe Berthon},
title = {Sch\'ema nonlin\'eaire pour l'approximation num\'erique d'un syst\`eme hyperbolique non conservatif},
journal = {Comptes Rendus. Math\'ematique},
pages = {1069--1072},
publisher = {Elsevier},
volume = {335},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02615-8},
language = {fr},
}
TY - JOUR AU - Christophe Berthon TI - Schéma nonlinéaire pour l'approximation numérique d'un système hyperbolique non conservatif JO - Comptes Rendus. Mathématique PY - 2002 SP - 1069 EP - 1072 VL - 335 IS - 12 PB - Elsevier DO - 10.1016/S1631-073X(02)02615-8 LA - fr ID - CRMATH_2002__335_12_1069_0 ER -
Christophe Berthon. Schéma nonlinéaire pour l'approximation numérique d'un système hyperbolique non conservatif. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1069-1072. doi : 10.1016/S1631-073X(02)02615-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02615-8/
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