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

Luigi C. Berselli (1) , Davide Catania (2) , Roger Lewandowski (3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 Dipartimento di Matematica [Universita di Brescia]
3 IRMAR - Institut de Recherche Mathématique de Rennes

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

Mots clés: Magnetohydrodynamics; Large Eddy Simulation; Deconvolution models

Domaines: Equations aux dérivées partielles [math.AP]

Luigi C. Berselli, Davide Catania, Roger Lewandowski. Convergence of approximate deconvolution models to the mean Magnetohydrodynamics Equations: Analysis of two models. Journal of Mathematical Analysis and Applications, 2013, 401 (2), pp.864-880. ⟨10.1016/j.jmaa.2012.12.051⟩. ⟨hal-00770945⟩