Implicit time schemes for compressible fluid models based on relaxation methods

David Coulette (1, 2) , Emmanuel Franck (1, 2) , Philippe Helluy (1, 2) , Ahmed Ratnani (3) , Eric Sonnendrücker (4, 3)

1 TONUS - TOkamaks and NUmerical Simulations
2 IRMA - Institut de Recherche Mathématique Avancée
3 IPP - Max-Planck-Institut für Plasmaphysik [Garching]
4 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

In this work, we are interested in the implicit discretization of compressible fluid models. When applied to this type of models, standard implicit schemes suffer from a lack of efficiency due to the ill-conditioning of the associated matrices. In this paper we propose an alternative strategy based on a relaxation method coupled with an implicit scheme. This method allows us to approximate the full complex problem by a collection of simpler ones than we can solve with standard methods. We obtain eventually a second order implicit method with some additional parallelism able to treat hyperbolic systems with small diffusion .

Domaines: Analyse numérique [math.NA]

David Coulette, Emmanuel Franck, Philippe Helluy, Ahmed Ratnani, Eric Sonnendrücker. Implicit time schemes for compressible fluid models based on relaxation methods. Computers and Fluids, 2019, 188, pp.70-85. ⟨10.1016/j.compfluid.2019.05.009⟩. ⟨hal-01514593⟩