Sub-grid modelling for a diffusive lattice gas

Vincent Labarre (1, 2) , Bérengère Dubrulle (2) , Didier Paillard (1)

1 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
2 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes

We address the sub-grid modelling problem of a simple two-dimensional diffusive lattice gas. We observe that the temporal variation of the coarse-grained current knowing the values of the coarse-grained density, its gradient, and the coarse-grained current is a Gaussian random variable in the low current limit. For this limit, we propose a simple sub-grid model based on a stochastic relaxation equation for the coarse-grained current that takes into account the size of the meshes. The method employed here may be suitable to other systems where we need to represent the small-scale dynamics, as far as the locality of the coarse-grained dynamics is verified.

Domaines: Planète et Univers [physics]

Vincent Labarre, Bérengère Dubrulle, Didier Paillard. Sub-grid modelling for a diffusive lattice gas. Journal of Physics A: Mathematical and Theoretical, 2020, 53 (40), ⟨10.1088/1751-8121/aba577⟩. ⟨hal-02984243⟩