Energy stable numerical methods for porous media flow type problems

Cancès, Clément

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.2516/ogst/2018067

Title :

Energy stable numerical methods for porous media flow type problems

Author(s) :

Cancès, Clément [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles

Pages :

Publisher :

Institut Français du Pétrole (IFP)

Publication date :

2018

ISSN :

1294-4475

HAL domain(s) :

Physique [physics]

English abstract : [en]

Many problems arising in the context of multiphase porous media flows that take the form of degenerate parabolic equations have a dissipative structure, so that the energy of an isolated system is decreasing along time. ...
Show more >Many problems arising in the context of multiphase porous media flows that take the form of degenerate parabolic equations have a dissipative structure, so that the energy of an isolated system is decreasing along time. In this paper, we discuss two approaches to tune a rather large family of numerical method in order to ensure a control on the energy at the discrete level as well. The first methodology is based on upwinding of the mobilities and leads to schemes that are unconditionally positivity preserving but only first order accurate in space. We present a second methodology which is based on the construction of local positive dissipation tensors. This allows to recover a second order accuracy w.r.t. space, but the preservation of the positivity is conditioned to some additional assumption on the nonlinearities. Both methods are based on an underlying numerical method for a linear anisotropic diffusion equation. We do not suppose that this building block is monotone.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :