Spectral magnetohydrodynamic simulations of the sun and stars

Abstract
The purpose of this lecture is two fold: first, to describe a powerful numerical technic, namely the spectral method, to solve the compressible (anelastic) magnetohydrodynamic (MHD) equations in spherical geometry and then to discuss some recent numerical applications to study stellar dynamics and magnetism. We thus start by describing the semi-implicit, anelastic spherical harmonic (ASH) code. In this code, the main field variables are projected into spherical harmonics for their horizontal dimensions and into Chebyshev polynomials for their radial direction. We then present, high resolution 3-D MHD simulations of the convective region of A- and G-type stars in spherical shells. We have chosen to model A and G-type stars because they represent good proxies to study and understand stellar dynamics and magnetism given their strikingly different internal "up-side-down" structure and magnetic activity level. In particular, we discuss the nonlinear interactions between turbulent convection, rotation and magnetic fields and the possibility for such flows and fields to lead to dynamo action. We find that both core and envelope turbulent convective zones are efficient at inducing strong mostly non-axisymmetric fields near equipartition but at the expense of damping the differential rotation present in the purely hydrodynamic progenitor solutions.