Approximate deconvolution models for magnetohydrodynamics

Abstract. We consider the family of approximate deconvolution models (ADM) for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove existence and uniqueness of solutions, we prove that the solutions to the ADM-MHD equations converge to the solution of the MHD equations in a weak sense as the averaging radii converge to zero, and we derive a bound on the modeling error. We prove that the energy and helicity of the models are conserved, and the models preserve the Alfvén waves. We provide the results of the computational tests, that verify the accuracy and physical fidelity of the models. The flow of an electrically conducting fluid is affected by Lorentz forces, induced by the interaction of electric currents and magnetic fields in the fluid. The Lorentz forces can be used to control the flow and to attain specific engineering design goals such as flow stabilization, suppression or delay of flow separation, reduction of near-wall turbulence and skin friction, drag reduction and thrust generation. There is a large body of literature dedicated to both experimental and theoretical investigations on the influence of electromagnetic force on flows (see e.g., Direct numerical simulation of a 3d turbulent flow is often not computationally economical or even feasible. On the other hand, the largest structures in the flow (containing most of the flow's energy) are responsible for much of the mixing and most of the flow's momentum transport. This led to various numerical regularizations; one of these is Large Eddy Simulation (LES

Architecture of Approximate Deconvolution Models of Turbulence

This report presents the mathematical foundation of approximate deconvolution LES models together with the model phenomenology downstream of the theory. This mathematical foundation now begins to be complete for the incompressible Navier–Stokes equations. It is built upon averaging, deconvolving and addressing closure so as to obtain the physically correct energy and helicity balances in the LES model. We show how this is determined and how correct energy balance implies correct prediction of turbulent statistics. Interestingly, the approach is simple and thus gives a road map to develop models for more complex turbulent flows. We illustrate this herein for the case of MHD turbulence.https://nsuworks.nova.edu/cnso_math_facbooks/1010/thumbnail.jp