We study the closure of reduced MHD models, such as the ones which are used in the modeling of Tokamaks and ITER, see Franck et al. (ESAIM: M2AN 49(5), 2015) and Guillard (2015) and references therein. We show how to modify the entropy moment methods to obtain a hierarchy of Navier–Stokes like models in potential formulation with a correct energy balance. Our procedure is well adapted to the complicated geometry of the torus. We obtain mainly two original results. One is a comparison principle between all these models: it explains that the dynamics of a reduced model is a lower bound of the dynamics of the initial model. The other one the existence of a weak solution to some of these complicate models adapted to the Tokamak geometry.
Journal of Mathematical Fluid Mechanics – Springer Journals
Published: Apr 27, 2017
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