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We consider two Large Eddy Simulation (LES) models for the approximation oflarge scales of the equations of Magnetohydrodynamics (MHD in the sequel). Westudy two $\alpha$-models, which are obtained adapting to the MHD the approachby Stolz and Adams with van Cittert approximate deconvolution operators. First,we prove existence and uniqueness of a regular weak solution for a system withfiltering and deconvolution in both equations. Then we study the behavior ofsolutions as the deconvolution parameter goes to infinity. The main result ofthis paper is the convergence to a solution of the filtered MHD equations. Inthe final section we study also the problem with filtering acting only on thevelocity equation.

Convergence of approximate deconvolution models to the mean Magnetohydrodynamics Equations: Analysis of two models