Approximate Deconvolution with Correction - A High Fidelity Model for Magnetohydrodynamic Flows at High Reynolds and Magnetic Reynolds Numbers

We propose a model for magnetohydrodynamic flows at high Reynolds and magnetic Reynolds numbers. The system is written in the Elsasser variables so that the decoupling method of [C. Trenchea, Unconditional stability of a partitioned IMEX method for magnetohydrodynamic flows, Appl. Math. Lett. 27 (2014), 97-100] can be used. This decoupling method is only first-order accurate, so the proposed model aims at improving the temporal accuracy (from first to second order), as well as reducing the modeling error of the existing turbulence model. This is done in the framework of the recently developed LES-C turbulence models [A. E. Labovsky, Approximate deconvolution with correction: A member of a new class of models for high Reynolds number flows, SIAM J. Numer. Anal. 58 (2020), 5, 3068-3090]. We show the model to be unconditionally stable and numerically verify its superiority over its most natural competitor.