Globally divergence-free spectral-DG methods for MHD equations on cylindrical coordinates

We propose a class of high order globally divergence-free spectraldiscontinuous Galerkin (DG) method for ideal magnetohydrodynamic (MHD) equations and resistive MHD equations on cylindrical coordinates (r, , z).Because the particular physical flows are toroidal symmetry or slow changes in the toroidal direction, the Fourier spectral method is adopted in the -direction and DG approximation is applied in the (r, z) plane.In particular, to satisfy the divergence-free property on cylindrical coordinates, we deform the induction equation and define the magnetic field components at interfaces.Moreover, employing a set of specially designed constraint-preserving schemes and magnetic field reconstruction techniques, we construct a general framework of the globally divergence-free spectral-DG method up to arbitrarily high order.Numerical experiments verify the robustness and efficacy of our methods.