OSAMOAL: optimized simulations by adapted models using asymptotic limits

Anne-Céline Boulanger (1) , Clément Cancès (2, 3) , Hélène Mathis (4) , Khaled Saleh (2, 5, 6, 7) , Nicolas Seguin (2)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
2 LJLL - Laboratoire Jacques-Louis Lions
3 RAPSODI - Reliable numerical approximations of dissipative systems
4 LMJL - Laboratoire de Mathématiques Jean Leray
5 ICJ - Institut Camille Jordan
6 UCBL - Université Claude Bernard Lyon 1
7 MMCS - Modélisation mathématique, calcul scientifique

We propose in this work to address the problem of model adaptation, dedicated to hyper- bolic models with relaxation and to their parabolic limit. The goal is to replace a hyperbolic system of balance laws (the so-called fine model) by its parabolic limit (the so-called coarse model), in delimited parts of the computational domain. Our method is based on the construction of asymptotic preserving schemes and on interfacial coupling methods between hyperbolic and parabolic models. We study in parallel the cases of the Goldstein-Taylor model and of the p-system with friction.

Mots clés: hyperbolic systems; parabolic limit; asymptotic preserving schemes; interfacial coupling

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Céline Boulanger, Clément Cancès, Hélène Mathis, Khaled Saleh, Nicolas Seguin. OSAMOAL: optimized simulations by adapted models using asymptotic limits. ESAIM: Proceedings and Surveys, 2012, 38, pp.183-201. ⟨10.1051/proc/201238010⟩. ⟨hal-00733865⟩