Large eddy simulation for turbulent magnetohydrodynamic flows

We investigate the mathematical properties of a model for the simulation of large eddies in turbulent, electrically conducting, viscous, incompressible flows. We prove existence and uniqueness of solutions for the simplest (zeroth) closed MUD model (1.7), we show that its solutions converge to the solution of the MUD equations as the averaging radii converge to zero, and derive a bound on the modeling error. Furthermore, we show that the model preserves the properties of the 3D MUD equations: the kinetic energy and the magnetic helicity are conserved, while the cross helicity is approximately conserved and converges to the cross helicity of the MUD equations, and the model is proven to preserve the Alfven waves, with the velocity converging to that of the MUD, as delta(1), delta(2) tend to zero. We perform computational tests that verify the accuracy of the method and compare the conserved quantities of the model to those of the averaged MUD. (C) 2010 Elsevier Inc. All rights reserved.