Numerical solution of the nonlinear electrodynamics in MHD regimes with magnetic Reynolds number near one

In magnetohydrodynamic (MHD) regimes of plasmas with magnetic Reynolds number comparable to one, electrodynamics exhibits a nonlinear characteristic. In the present paper, the electrodynamics has been discretized utilizing a finite-element method. The problem unknown is the electric scalar potential. Nonlinearity is caused by the dependence of the electric transport parameters and of the source terms on the magnetic flux density. Different approaches are evaluated to deal with the nonlinearity. The model has been coupled with a solver of the Navier-Stokes equations. The MHD interaction in the boundary layer of an hypersonic flight has been analyzed.