On the Leray-deconvolution model for the incompressible magnetohydrodynamics equations

We extend Leray-α-deconvolution modeling to the incompressible magnetohydrodynamics (MHD). The resulting model is shown to be well-posed, and have attractive limiting behavior both in its filtering radius and order of deconvolution. Additionally, we present and study a numerical scheme for the model, based on an extrapolated Crank-Nicolson finite element method. We show the numerical scheme is unconditionally stable, preserves energy and cross-helicity, and optimally converges to the MHD solution. Numerical experiments are provided that verify convergence rates, and test the scheme on benchmark problems of channel flow over a step and the Orszag-Tang vortex problem.