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 that can be solved with standard methods. We obtain eventually a second order implicit method with some additional parallelism able to treat hyperbolic systems with small diffusion.     «

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 that can be solved with standard methods. We obtai...     »