Luigi C. Berselli, Davide Catania, Roger Lewandowski
Published 2012-06-07Version 1
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.
Convergence of approximate deconvolution models to the filtered Navier-Stokes Equations
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations
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