Navier-Stokes hierarchies of reduced MHD models in Tokamak geometry

Bruno Després (1) , Rémy Sart (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ESILV - École Supérieure d'Ingénierie Léonard de Vinci

We study the closure of reduced MHD models. We show how to modify the entropy moment methods to obtain a hierarchy of models of Navier-Stokes type with a correct energy balance. Our procedure is based on the entropy and well adapted to the complicated geometry of the torus. A new correction term due to the geometry is derived, what is important for the stability of the model. We prove the existence of a weak solution to some of these models by similarity with Navier-Stokes theory in potential formulation. We finally obtain a comparison principle between all these models.

Mots clés: reduced MHD models; mathematical stability; entropy method; energy conservation

Domaines: Analyse numérique [math.NA]

Bruno Després, Rémy Sart. Navier-Stokes hierarchies of reduced MHD models in Tokamak geometry. Journal of Mathematical Fluid Mechanics, 2018, 20, pp.329-357. ⟨hal-00796425v2⟩